Factor each polynomial. 9(a-4)^{2}+30(a-4)+25

Sam Longoria

Sam Longoria

Answered question

2021-12-12

Factor each polynomial.
9(a4)2+30(a4)+25

Answer & Explanation

Carl Swisher

Carl Swisher

Beginner2021-12-13Added 28 answers

Step 1
Factoring a polynomial is to reduce it to a product of its irreducible factor. For example x21 can be factored as (x-1)(x+1) while x2+1 cannot be factored further. If a polynomial has x-a as its factor then the polynomial has a zero at x=a.
The expression x2+ax+bx+ab can be factored as (x+a)(x+b). Use this to factor the quadratic after expanding the terms in the parenthesis.
Step 2
Given polynomial is 9(a4)2+30(a4)+25. Expanding the parenthesis terms, simplify and then use (AB)2=A22AB+B2 to factor the polynomial.
9(a4)2+30(a4)+25=9(a2+168a)+30a120+25
=9a2+14472a+30a95
=9a242a+49
=(3a)2273a+72
=(3a7)2
Hence, the given polynomial in factored form is (3a7)2.

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