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Chapter 6: Q 74E (page 589)

In the following exercises, factor each trinomial of the form

x2+bx+C.6n-7+n虏

Short Answer

Expert verified

The binomial factors of the equations are(n+7)(n-1).

Step by step solution

01

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

The given equation is

6n-7+n虏

The general form is

n虏+6n-7

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 7, and their sum is 6. Because the third term sign is negative, the sum seems to be a difference.

Factors71Difference6

So form of binomial is (n7)(n1).

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:

(n+7)(n-1)

04

Step 4. Checking the factors

Check:Multiplythefactors.(n+7)(n-1)=n虏-n+7n-7[Multiply]=n虏+6n-7True[Grouptheliketerms]

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