Exercise 47 Page 83

Start by identifying the values of b and c.

(x+4)(x+5)

Practice makes perfect

To factor the quadratic expression, we will start by identifying the values of a, b, and c. x^2+9x+20 ⇔ 1x^2+ 9x+ 20 For our expression we have that a= 1, b= 9, and c= 20. To factor a quadratic expression with leading coefficient a= 1, we need to find two factors of c= 20 whose sum is b= 9. Since 20 is a positive number, we will only consider factors with the same sign — both positive or both negative — so that their product is positive.

Factor Pair	Product	Sum
1 and 20	^(1* 20) 20	1+20 21
- 1 and - 20	^(- 1* (- 20)) 20	^(- 1+(- 20)) - 21
2 and 10	^(2* 10) 20	2+10 12
- 2 and - 10	^(- 2* (- 10)) 20	^(- 2+(- 10)) - 12
4 and 5	^(4 * 5) 20	^(4+5) 9
- 4 and - 5	^(- 4* (- 5)) 20	^(- 4+(- 5)) - 9

The integers whose product is 20 and whose sum is 9 are 4 and 5. x^2+9x+20 ⇔ (x+4)(x+5) Let's use a graphing calculator to confirm our answer. To do so, we will graph the related functions in the same coordinate plane.