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Algebra Help: Terms Factors And Coefficients

Review real example questions for Terms Factors And Coefficients in Algebra.

Question 1 / 10

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What is the coefficient of $y$ in the expression $2y^2-y+6$ ?

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Question 1

What is the coefficient of $y$ in the expression $2y^2-y+6$ ?

$2$
$-1$ (correct answer)
$1$
$-y$

Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify coefficients. A coefficient is the numerical part of a term that's multiplied by the variable(s): in the term 3x², the coefficient is 3 because it's the number being multiplied by x². Remember that coefficients include their sign, so in -5x, the coefficient is -5, not 5. To find the coefficient of y in 2y² - y + 6, we look for the term that contains y (without higher powers). That term is -y. The coefficient is the number part that's multiplied by the variable, which is -1. If you don't see a number written, like in just 'x', the coefficient is 1! Choice B is correct because it properly identifies the coefficient as -1, following the definition that 'invisible' coefficients include the sign. You've got it! Choice C misses that when we don't see a number, like in '-y', there's still a coefficient—it's -1. These 'invisible' coefficients are easy to overlook! To find a coefficient, first locate the term with the variable you're looking for, then identify just the number part (including the sign). If you don't see a number, the coefficient is 1 (for terms like x) or -1 (for terms like -x). Write out that 'invisible 1' when learning, and it'll help!

Question 2

In the expression $(x + 4)(x - 2)$ , what are the factors?

$x+4x-2$
$x,\ 4,\ x,\ -2$
$(x+4)\ \text{and}\ (x-2)$ (correct answer)
$x+4,\ x,\ -2$

Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify factors. Factors are parts of an expression that are multiplied together: when you see multiplication (either with · or parentheses next to each other), you're looking at factors. For example, in 4(x + 3), the factors are 4 and (x + 3) because they're being multiplied. In (x + 4)(x - 2), we can see what's being multiplied together: it's (x + 4) times (x - 2). This means the factors are (x + 4) and (x - 2). Remember, factors are connected by multiplication, while terms are connected by addition and subtraction. Choice A is correct because it properly identifies the factors as (x + 4) and (x - 2), following the definition that factors are the multiplied parts. You've got it! Choice B is close, but it confuses terms with factors: it lists x, 4, x, -2 which are terms inside the parentheses, but the question asks for the main factors. Remember: terms are added/subtracted, factors are multiplied! Think of terms as 'ingredients being added together' and factors as 'ingredients being multiplied together.' In (x + 4)(x - 2), you're multiplying (x + 4) times (x - 2), so those are factors. But when you expand to x² + 2x - 8, you're adding x², 2x, and -8, so those are terms. Choice D treats parts inside parentheses as separate terms, but actually (x + 4) is grouped as one factor here. Terms are only separated by + and - at the outermost level!

Question 3

What is the coefficient of $a$ in the expression $-5a+2a^2-1$ ?

$-5$ (correct answer)
$2$
$5$
$-5a$

Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify coefficients. A coefficient is the numerical part of a term that's multiplied by the variable(s): in the term $3x^2$ , the coefficient is 3 because it's the number being multiplied by $x^2$ . Remember that coefficients include their sign, so in $-5x$ , the coefficient is -5, not 5. To find the coefficient of $a$ in $-5a + 2a^2 - 1$ , we look for the term that contains $a$ . That term is $-5a$ . The coefficient is the number part that's multiplied by the variable, which is -5 with the sign. Choice A is correct because it properly identifies the coefficient as -5, following the definition that coefficients include their sign. You've got it! Choice B is close, but it forgets to include the sign: the coefficient is -5, not 5. The minus sign is part of the coefficient! This is a super common mistake, so watch out for it. To find a coefficient, first locate the term with the variable you're looking for, then identify just the number part (including the sign). If you don't see a number, the coefficient is 1 (for terms like $a$ ) or -1 (for terms like $-a$ ). Write out that 'invisible 1' when learning, and it'll help!

Question 4

In the expression $-x+9$ , what is the coefficient of $x$ ?

$1$
$-1$ (correct answer)
$-x$
$9$

Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify coefficients. A coefficient is the numerical part of a term that's multiplied by the variable(s): in the term 3x², the coefficient is 3 because it's the number being multiplied by x². Remember that coefficients include their sign, so in -5x, the coefficient is -5, not 5. To find the coefficient of x in -x + 9, we look for the term that contains x. That term is -x. The coefficient is the number part that's multiplied by the variable, which is -1. If you don't see a number written, like in just '-x', the coefficient is -1! Choice B is correct because it properly identifies the coefficient as -1, following the definition that coefficients include their sign. You've got it! Choice A is close, but it misses that when we don't see a number, like in '-x', there's still a coefficient—it's -1, not 1. These 'invisible' coefficients are easy to overlook! To find a coefficient, first locate the term with the variable you're looking for, then identify just the number part (including the sign). If you don't see a number, the coefficient is 1 (for terms like x) or -1 (for terms like -x). Write out that 'invisible 1' when learning, and it'll help!

Question 5

What are the terms in $3x^2-5x+2$ ?

$3x^2,\;5x,\;2$
$3x^2,\;-5x,\;2$ (correct answer)
$3,\;x^2,\;-5,\;x,\;2$
$3x^2-5x,\;2$

Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify terms. Terms are the parts of an expression that are added or subtracted from each other: think of them as the separate 'chunks' connected by + or - signs. For example, in 3x² - 5x + 2, there are three terms: 3x², -5x, and 2 (notice that the -5x includes the minus sign). Let's look at the expression 3x² - 5x + 2 and find the terms. Terms are separated by + or - signs (at the main level, not inside parentheses): starting from the left, we have 3x², then -5x, and finally +2. That gives us 3 terms total. Choice B is correct because it properly identifies the terms as 3x², -5x, 2, following the definition that terms include their signs. You've got it! Choice A is close, but it forgets to include the sign: the term is -5x, not 5x. The minus sign is part of the term! This is a super common mistake, so watch out for it. Don't forget: signs matter! The term in x² - 4x isn't 4x, it's -4x. Always include the sign that comes right before the term—that sign is part of it. This is one of the most common mistakes in algebra, so being careful here will save you lots of points!

Question 6

What is the coefficient of the quadratic term in the expression $4 - 2x + 9x^2$ ?

$9$ (correct answer)
$-2$
$9x^2$
$4$

Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify coefficients. A coefficient is the numerical part of a term that's multiplied by the variable(s): in the term 3x², the coefficient is 3 because it's the number being multiplied by x². Remember that coefficients include their sign, so in -5x, the coefficient is -5, not 5. To find the coefficient of the quadratic term in 4 - 2x + 9x², we look for the term that contains x² (the quadratic). That term is +9x². The coefficient is the number part that's multiplied by the variable, which is 9 (with sign, but it's positive). If you don't see a number written, like in just 'x', the coefficient is 1! Choice A is correct because it properly identifies the coefficient as 9, following the definition that it's the numerical multiplier of the x² term. You've got it! Choice C is close, but it gives the entire term 9x² when the question asks just for the coefficient (which would be 9, the number part). The coefficient is only the numerical part, not the variable. Choice B forgets that the quadratic term is 9x² with coefficient 9, not -2 (which is for the x term). This is a super common mistake, so watch out for it. To find a coefficient, first locate the term with the variable you're looking for, then identify just the number part (including the sign). If you don't see a number, the coefficient is 1 (for terms like x) or -1 (for terms like -x). Write out that 'invisible 1' when learning, and it'll help!

Question 7

What is the constant term in $3k^3-2k^2+k$ ?

$k$
$0$ (correct answer)
$3$
$-2$

Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify the constant term. The constant term is the part of the expression that doesn't have any variables—it's just a number by itself, like the +2 at the end of 3x² - 5x + 2. The constant term is the number that stands alone without any variables attached. In 3k³ - 2k² + k, looking through each part, there is no constant term, so it's 0. This is different from the coefficients, which are the numbers multiplied by variables. Choice B is correct because it properly identifies the constant term as 0, following the definition that it's the number without variables. You've got it! Choice C forgets that the constant term is the number without any variables. In this expression, there's none, so 0, not 3 (which is a coefficient). A quick check: count your terms by counting how many parts would be separated if you put the expression in a calculator with clear + and - between them. For 3k³ - 2k² + k, you'd enter it as three separate chunks—all with variables, so constant is 0!

Question 8

What is the coefficient of $x$ in the expression $x+5$ ?

$0$
$1$ (correct answer)
$x$
$5$

Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify coefficients. A coefficient is the numerical part of a term that's multiplied by the variable(s): in the term 3x², the coefficient is 3 because it's the number being multiplied by x². Remember that coefficients include their sign, so in -5x, the coefficient is -5, not 5. To find the coefficient of x in x + 5, we look for the term that contains x. That term is x (or +x). The coefficient is the number part that's multiplied by the variable, which is 1. If you don't see a number written, like in just 'x', the coefficient is 1! Choice C is correct because it properly identifies the coefficient as 1, following the definition that 'invisible' coefficients are 1. You've got it! Choice A gives 0, but that would mean no x term at all; here there is an x with coefficient 1. These 'invisible' coefficients are easy to overlook! To find a coefficient, first locate the term with the variable you're looking for, then identify just the number part (including the sign). If you don't see a number, the coefficient is 1 (for terms like x) or -1 (for terms like -x). Write out that 'invisible 1' when learning, and it'll help!

Question 9

In the expression $6x(x-3)$ , what are the factors being multiplied?

$6x$ and $x-3$ are the terms
$6x-3$ and $x$
$6x$ and $(x-3)$ (correct answer)
$6,\;x,\;x,\;-3$ are the terms

Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify factors. Factors are parts of an expression that are multiplied together: when you see multiplication (either with · or parentheses next to each other), you're looking at factors. For example, in 4(x + 3), the factors are 4 and (x + 3) because they're being multiplied. In 6x(x - 3), we can see what's being multiplied together: it's 6x and (x - 3). This means the factors are 6x and (x - 3). Remember, factors are connected by multiplication, while terms are connected by addition and subtraction. Choice A is correct because it properly identifies the factors as 6x and (x - 3), following the definition that factors are the parts being multiplied. You've got it! Choice D confuses terms with factors: it lists 6x and x-3 as terms, but the question asks for factors. Remember: terms are added/subtracted, factors are multiplied! Think of terms as 'ingredients being added together' and factors as 'ingredients being multiplied together.' In 2(x + 3), you're multiplying 2 times (x + 3), so those are factors. But when you expand to 2x + 6, you're adding 2x and 6, so those are terms.

Question 10

What is the coefficient of $x$ in the expression $x^2 - 4x + 1$ ?

$-4x$
$4$
$-4$ (correct answer)
$1$

Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify coefficients. A coefficient is the numerical part of a term that's multiplied by the variable(s): in the term 3x², the coefficient is 3 because it's the number being multiplied by x². Remember that coefficients include their sign, so in -5x, the coefficient is -5, not 5. To find the coefficient of x in x² - 4x + 1, we look for the term that contains x. That term is -4x (with sign). The coefficient is the number part that's multiplied by the variable, which is -4 (with sign). If you don't see a number written, like in just 'x', the coefficient is 1! Choice C is correct because it properly identifies the coefficient as -4, following the definition that coefficients include the sign and are the numerical multiplier. You've got it! Choice B is close, but it forgets to include the sign: the coefficient is -4, not 4. This is a super common mistake, so watch out for it. To find a coefficient, first locate the term with the variable you're looking for, then identify just the number part (including the sign). If you don't see a number, the coefficient is 1 (for terms like x) or -1 (for terms like -x). Write out that 'invisible 1' when learning, and it'll help! Don't forget: signs matter! The term in x² - 4x isn't 4x, it's -4x. Always include the sign that comes right before the term—that sign is part of it. This is one of the most common mistakes in algebra, so being careful here will save you lots of points!