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Precalculus Mathematics for Calculus
Found in: Page 33
Precalculus Mathematics for Calculus

Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508

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Short Answer

To factor the trinomial x2+7x+10, we look for two integers whose product is _____ and whose sum is _____. These integers are _____ and _____, so the trinomial factors as _______.

To factor the trinomial x2+7x+10, we look for two integers whose product is 10 and whose sum is 7. These integers are 5 and 2 , so the trinomial factors as x2+7x+10=x+5x+2

See the step by step solution

Step by Step Solution

Step 1. Apply the concept of factoring trinomials.

To factor a trinomial of the form ax2+bx+c, we note that

x+rx+s=x2+r+sx+rs

So, we need to choose numbers r and s so that r+s=b and rs=c.

Step 2. Analyze the trinomial.

Given x2+7x+10

This is of the form ax2+bx+c where b=7 and c=10

The factorization of the trinomial will be x+rx+s=x2+r+sx+rs

So, we need to choose numbers r and s so that r+s=b and rs=c.

Step 3. Find the integers to factor the trinomial.

We need to choose integers r and s so that r+s=7 and rs=10.

By trial and error we find that the two integers are r=5,s=2

r+s=5+2=7

rs=52=10

Step 4. Factor the trinomial.

The factorization of the trinomial is

x2+7x+10=x+rx+sx2+7x+10=x+5x+2

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