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Chapter 11: Q 77E (page 1069)

In the following exercises, factor each trinomial of the form

x2+bx+cx2-12-11x

Short Answer

Expert verified

The binomial factors of the equations are(x-12)(x+1).

Step by step solution

01

Step 1. Given information and rewriting the equation in general from  

The given equation is

x2-12-11x

The general form is

x2-11x-12

02

Step 2. Writing factors as two binomial with n. 

The factors should be written as two binomials with n as the first term.

(n)(n)

The product of the two numbers is -12, and their sum is -11. Because the third term sign is negative, the sum seems to be a difference.

Factors121Difference11

The binomial factors are as follows: (x12)(x1)

03

Step 3. Finding factors  

The larger binomial second term is also positive because the second trinomial term is positive.

Because the third trinomial term is negative, the binomial signs are transposed.

The binomial factors are as follows:

(x-12)(x+1)

04

Step 4. Checking the factors  

Check:Multiplythefactors.(x-12)(x+1)=x虏-12x+x-12[Multiply]=x虏-11x-12True[Grouptheliketerms]

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