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Chapter 6: Q 82E (page 589)

In the following exercises, factor each trinomial of the form

x2+bxy+cy2p2-2pq-35q2

Short Answer

Expert verified

The binomial factors of the equations are(p-7q)(p+5q)

Step by step solution

01

Step 1. Given information

The given equation

p2-2pq-35q2

02

Step 2. Writing factors as two binomial with first term p and second term q.

The factors should be written as two binomials with first term p and second term q.

(pq)(pq)

The product of the two numbers is 35,and their sum is 2. Because the third term sign is negative, the sum seems to be a difference.

Factors35715Difference642

So form of binomial is(p7q)(p5q).

03

Step 3. Finding factors  

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

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

The binomial factors are as follows:

(p-7q)(p+5q)

04

Step 4. Checking the factors 

Check:Multiplythefactors.(p-7g)(p+5g)=p虏+5pq-7pq-35q虏True[Multiply]=p虏-2pq-35q虏[Grouptheliketerms]

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