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Chapter 11: Q. 355 (page 1069)

In the following exercises, factor each trinomial of the form x2+bx+c.

a2+14a+33

Short Answer

Expert verified

The factored form of the polynomial is (a+11)(a+3).

Step by step solution

01

Step 1. Given Information

We are given a polynomial,

a2+14a+33

02

Step 2. Factorizing the polynomial 

Using the product of acmethod in factorizing the polynomial of form ax2+bx+c, we get

11脳3=3311+3=14

So, Splitting the middle term,

localid="1644849982369" a2+14a+33=a2+11a+3a+33

Grouping terms, we get

localid="1644849962131" a2+14a+33=a2+11a+3a+33

Factoring out GCF from groups, we get

localid="1661956442984" a2+11a+3a+33=a(a+11)+3(a+11)

Again, factoring out GCF, we get

localid="1644850003709" a2+14a+33=(a+11)(a+3)

03

Step 3. Checking the factorization

Multiplying the factors,

(a+11)(a+3)=a2+14a+33a(a+3)+11(a+3)=a2+14a+33a2+3a+11a+33=a2+14a+33a2+14a+33=a2+14a+33LHS=RHS

Hence the factorization is correct.

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