Algebra 1 : Factoring Polynomials

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #71 : How To Factor A Polynomial

Factor .

Possible Answers:

Cannot be factored

Correct answer:

Explanation:

This may look complicated at first, but it's just a special case of a polynomial called a 'difference of squares.' That means that there are two terms, one is negative, and they are both perfect squares. In this case, the negative is -16. The was to factor this type of polynomial is to follow this formula:

(square root of the positive perfect square + square root of the negative perfect square) x (square root of the positive perfect square - square root of the negative perfect square).

This gives the answer  for this problem.

Remember, you can always check your work by foiling the factored expression out to make sure it matches the original polynomial.

Example Question #71 : How To Factor A Polynomial

Solve for :  

Possible Answers:

Correct answer:

Explanation:

First isolate all terms with x to one side and keep all other terms on the other side.

To this end, multiple both sides of the equation by c.

This gives

.

Then factor x out of the right side of the equation to get

.

Finally, divide both sides of the equation by  to get the answer.

Example Question #381 : Polynomials

Factor the polynomial:  

Possible Answers:

Correct answer:

Explanation:

The common factor in this problem is only , because each number in this term share the same factor.  

By pulling this term out of the expression, we need to find , and  that would match the terms of the problem.

Determine .  Divide by  on both sides.

Determine .

Determine .

Resubstitute the variables.

This means that .

The answer is:  

Example Question #72 : How To Factor A Polynomial

Factor the following:

Possible Answers:

no factors

Correct answer:

Explanation:

To factor a polynomial, first express the polynomial in the form .  Then, if , you need to find factors of  that add up to .  Your answer will use those factors.  The best answer for the equation above is:

Example Question #392 : Variables

Factor the following:

Possible Answers:

no factors

Correct answer:

Explanation:

To factor a polynomial, first express the polynomial in the form .  Then, if , you need to find factors of  that add up to .  Your answer will use those factors.  The best answer for the equation above is:

Example Question #73 : How To Factor A Polynomial

Factor the following:

Possible Answers:

Correct answer:

Explanation:

To factor a polynomial, first express the polynomial in the form .  Then, if , you need to find factors of  that add up to b.  Your answer will use those factors.  The best answer for the equation above is:

Example Question #73 : How To Factor A Polynomial

Factor the following:

Possible Answers:

Correct answer:

Explanation:

To factor a polynomial, first express the polynomial in the form .  Then, if , you need to find factors of  that add up to b.  Your answer will use those factors.  The best answer for the equation above is:

Example Question #4621 : Algebra 1

Factor the following:

Possible Answers:

Correct answer:

Explanation:

To factor a polynomial, first express the polynomial in the form .  Then, if , you need to find factors of  that add up to b.  Your answer will use those factors.  The best answer for the equation above is:

Example Question #71 : Factoring Polynomials

Factor the following polynomial.

Possible Answers:

Correct answer:

Explanation:

When factoring a polynomial, you have to determine the numbers that when multiplied together will equal the last term of the polynomial but when added together will equal the second term of the polynomial. 

The only factors of 9 are (1,3,9). The trick in this question is that the last term is positive, but the middle term is negative. The only way to achieve this is to make both of the factors negative, so when multiplied together they equal a positive. 

Example Question #391 : Variables

Factor: 

Possible Answers:

Correct answer:

Explanation:

To factor a quadratic trinomial, list factors of the quadratic  term and the constant (no variables) term, then combine them into binomials that when multiplied back out will give the original trinomial.

Here, the quadratic term has only one factorization: .

The constant term has factorizations of  and .

We know the constant term is positive, so the binomials both have the same operation in them (adding or subtracting), since a positive times a positive OR a negative times a negative will both give a positive result.

But since the middle term  is negative, both binomial factors must contain subtraction. And .

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