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Chapter 6: Problem 27

Factor each polynomial using the greatest common factor. If there is no common factor other than 1 and the polynomial cannot be factored, so state. $$13 y^{2}-25 y$$

Short Answer

Expert verified
The factored form of the polynomial \(13 y^{2}-25 y\) is \(y(13y - 25)\).

Step by step solution

01

Identify the greatest common factor

Find the greatest common factor (GCF) present in both terms. In this case, \(y\) is common to both terms. So the GCF between \(13y^{2}\) and \(-25y\) is \(y\).
02

Apply the GCF to each term

The application involves dividing each term by the GCF. Dividing \(13y^{2}\) by \(y\) gives \(13y\) and dividing \(-25y\) by \(y\) gives -25. Combined, we then get \(13y - 25\) as the result for this step.
03

Express the factored polynomial

Express the factored form of the polynomial. It's done by writing the result of step 2 in parentheses, multiplied by the GCF. Therefore the factored form of the polynomial \(13 y^{2}-25 y\) is \(y(13y - 25)\).

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Most popular questions from this chapter

Contain polynomials in several variables. Factor each polynomial completely and check using multiplication. $$3 x^{4}-9 x^{3} y+3 x^{2} y^{2}$$

Now let's move on to factorizations that may require two or more techniques. Factor completely, or state that the polynomial is prime. Check factorizations using multiplication or a graphing utility. $$3 x^{2}+243$$

Factor completely. $$x^{2}+8 x+16-25 a^{2}$$

Contain polynomials in several variables. Factor each polynomial completely and check using multiplication. $$x y-5 x+2 y-10$$

Now let's move on to factorizations that may require two or more techniques. Factor completely, or state that the polynomial is prime. Check factorizations using multiplication or a graphing utility. $$48 a^{4}-3 a^{2}$$
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