# The blank in the statement “To factor the trinomial x 2 + 7 x + 10 , we look for two integers whose product is _ and whose sum is _ . These integers are _ and _ , so the trinomial factors as _ ”.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.3, Problem 2E
To determine

## To fill: The blank in the statement “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                    _”.

Expert Solution

The complete statement is “To factor the trinomial x2+7x+10, we look for two integers whose product is 10_ and whose sum is 7_. These integers are 2_ and 5_, so the trinomial factors as (x+5)(x+2)_.

### Explanation of Solution

The given trinomial is x2+7x+10.

It is known that, the general form of trinomial is x2+bx+c.

To factor a trinomial choose numbers r and s such that r+s=b and rs=c. That is,

(x+r)(x+s)=x2+(r+s)x+rs

In the trinomial x2+7x+10, obtain two integers whose product is 10 and sum is 7.

Note that 5×2=10 and 5+2=7. That is, the two required integers are 5 and 2.

Therefore, the factorization will be as x2+7x+10=(x+5)(x+2).

Thus, the complete statement is “To factor the trinomial x2+7x+10, we look for two integers whose product is 10_ and whose sum is 7_. These integers are 2_ and 5_, so the trinomial factors as (x+5)(x+2)_.

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