Which shows factored completely by its GCF?
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College Algebra Quiz
Practice Factoring Out Greatest Common Factor Gcf in College Algebra with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.
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Which shows 25p3−10p2 factored completely by its GCF?
This quiz focuses on Factoring Out Greatest Common Factor Gcf, giving you a quick way to practice the rules, question types, and explanations that matter most for College Algebra.
Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.
Which shows 25p3−10p2 factored completely by its GCF?
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 25p^3 - 10p^2, the GCF is 5p^2, which, when factored out, results in the expression 5p^2(5p - 2). The correct choice, 5p^2(5p-2), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor '5p(5p^2-2p)', which misses the full variable power. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.
Identify the GCF and rewrite: 6x2y+9xy.
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 6x^2 y + 9xy, the GCF is 3xy, which, when factored out, results in the expression 3xy(2x + 3). The correct choice, 3xy(2x+3), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor '3y(2x^2+3x)', which misses the common x in both terms. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.
Identify the GCF and factor: 8m2n3+12mn2.
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 8m^2 n^3 + 12m n^2, the GCF is 4m n^2, which, when factored out, results in the expression 4m n^2(2m n + 3). The correct choice, 4m n^2(2m n + 3), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor '2m n(4m n^2 + 6n)', which misses the largest common coefficient. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.
Identify the GCF and rewrite: 7x2y−14xy2.
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 7x^2 y - 14x y^2, the GCF is 7x y, which, when factored out, results in the expression 7x y(x - 2y). The correct choice, 7x y(x-2y), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor '7y(x^2-2x y^2)', which misses the common x. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.
Identify the GCF and rewrite: 16m2n−24mn2.
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 16m^2 n - 24m n^2, the GCF is 8m n, which, when factored out, results in the expression 8m n(2m - 3n). The correct choice, 8m n(2m-3n), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor '8m^2 n(2-3n)', which misses the correct variable powers. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.
Choose the correct GCF for 36x2y and 48xy2 and factor it out.
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given terms, 36x^2 y and 48x y^2, the GCF is 12x y, which, when factored out, results in the expression 12x y(3x + 4y). The correct choice, 12x y(3x+4y), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor '6x y(6x+8y)', which misses the largest common factor. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.
Choose the correct GCF for 24a2b and 36ab2, then factor it out.
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given terms, 24a^2 b and 36a b^2, the GCF is 12ab, which, when factored out, results in the expression 12ab(2a + 3b). The correct choice, 12ab(2a+3b), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor '6ab(4a+6b)', which misses the largest common factor. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.
Which shows 3x2+6x factored completely by its GCF?
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 3x^2 + 6x, the GCF is 3x, which, when factored out, results in the expression 3x(x + 2). The correct choice, 3x(x+2), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor 'x(3x+6)', which misses the largest common coefficient. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.
Which shows 18x3y+12x2y2 factored completely by its GCF?
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 18x^3 y + 12x^2 y^2, the GCF is 6x^2 y, which, when factored out, results in the expression 6x^2 y(3x + 2y). The correct choice, 6x^2 y(3x+2y), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor '3x^2 y(6x+4y)', which misses the largest common factor. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.
What is the GCF of the terms in 20x4y2 and 30x2y3?
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. For the given terms, 20x^4 y^2 and 30x^2 y^3, the GCF is 10x^2 y^2. The correct choice, 10x^2 y^2, accurately represents the GCF, demonstrating understanding of the concept. A common mistake is selecting a non-greatest factor, seen in the distractor '5x^4 y^3', which does not divide both terms evenly. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.
How can −12x2−18x be simplified by factoring out the GCF?
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, -12x^2 - 18x, the GCF is -6x (or equivalently 6x with negatives inside), which, when factored out, results in the expression -6x(2x + 3). The correct choice, -6x(2x+3), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is ignoring the negative sign, seen in distractors that do not match the original expression. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.
Which shows 4x2+12x factored completely by its GCF?
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 4x^2 + 12x, the GCF is 4x, which, when factored out, results in the expression 4x(x + 3). The correct choice, 4x(x+3), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor 'x(4x+12)', which misses the largest common coefficient. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.
Which shows 14x2−21x factored completely by its GCF?
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 14x^2 - 21x, the GCF is 7x, which, when factored out, results in the expression 7x(2x - 3). The correct choice, 7x(2x-3), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor '7(2x^2-3x)', which misses the common x. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.
Which shows 8x3+4x factored completely by its GCF?
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 8x^3 + 4x, the GCF is 4x, which, when factored out, results in the expression 4x(2x^2 + 1). The correct choice, 4x(2x^2+1), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor 'x(8x^2+4)', which misses the largest common coefficient. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.
Factor out the GCF: 35x2y+49xy2.
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 35x^2 y + 49x y^2, the GCF is 7x y, which, when factored out, results in the expression 7x y(5x + 7y). The correct choice, 7x y(5x + 7y), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor 'x y(35x + 49y)', which misses the largest common coefficient. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.
Identify the GCF and factor: 10x3+15x2.
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 10x^3 + 15x^2, the GCF is 5x^2, which, when factored out, results in the expression 5x^2(2x + 3). The correct choice, 5x^2(2x + 3), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor '5x(2x^2 + 3x)', which misses the full variable power in the GCF. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.
Which of the following shows 24x2−36x factored completely by its GCF?
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 24x^2 - 36x, the GCF is 12x, which, when factored out, results in the expression 12x(2x - 3). The correct choice, 12x(2x - 3), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor '6x(4x - 6)', which misses the largest common coefficient. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.
Which shows 2x2y+8xy factored completely by its GCF?
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 2x^2 y + 8x y, the GCF is 2x y, which, when factored out, results in the expression 2x y(x + 4). The correct choice, 2x y(x+4), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor 'x y(2x+8)', which misses the largest common coefficient. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.
Factor out the GCF: 4xy+8x2y2.
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 4x y + 8x^2 y^2, the GCF is 4x y, which, when factored out, results in the expression 4x y(1 + 2x y). The correct choice, 4x y(1 + 2x y), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor '4x(y + 2x y^2)', which misses the common y in the second term properly. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.
Which expression shows 15xy+20y factored completely by its GCF?
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 15x y + 20 y, the GCF is 5 y, which, when factored out, results in the expression 5 y(3x + 4). The correct choice, 5 y(3x + 4), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor 'y(15x + 20)', which misses the largest common coefficient. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.