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Chapter 6: Q. 451 (page 638)

Factor completely:

9s2-12s+4.

Short Answer

Expert verified

The factored polynomial is,

(3s-2)2.

Step by step solution

01

Step 1. Given the information.

The polynomial function is,

9s2-12x+4.

02

Step 2. Factoring the polynomial.

9s2-12s+4

Splitting the middle term such that the sum of the terms is (-12)and the product of the terms is 36.

=9s2-6s-6s+4=(9s2-6s)-(6s-4)

Taking out the common factors,

=3s(3s-2)-2(3s-2)=(3s-2)(3s-2)=(3s-2)2

03

Step 3. Checking the solution.

(3s-2)2

Using the identity,(a-b)2=a2-2ab+b2,

role="math" localid="1644784547183" =(3s)2-2脳3s脳2+(2)2=9s2-12s+4

This is true.

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