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Chapter 6: Q 66E (page 589)

In the following exercises, factor each trinomial of the formx2+bx+c.

u2+101u+100

Short Answer

Expert verified

The factors are(u+1)(u+100).

Step by step solution

01

Step 1. Writing the expression

Write the factors as two binomials with first terms u.

localid="1644544034773" (u)(u).

02

Step 2. Finding the factors

We need to find two numbers whose product is 100and sum is 101.

Since 101is a prime number, we know that 1and 100are the only numbers whose product is 100and sum is 101.

Hence, the factorization of the trinomial is(u+1)(u+100).

03

Step 3. Check

Multiply the factorization to get the trinomial again.

(u+1)(u+100)=u2+100u+u+100(u+1)(u+100)=u2+101u+100

Thus, the obtained factorization is correct.

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