To factor the quadratic expression, we will start by identifying the values of a, b, and c.
44+15h+h^2 ⇔ 1h^2+ 15h+ 44
For our expression, we have that a= 1, b= 15, and c= 44.
To factor a quadratic expression with leading coefficient a= 1, we need to find two factors of c= 44 whose sum is b= 15. Since 44 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 44
^(1* 44) 44
1+44 45
- 1 and - 44
^(- 1* (- 44)) 44
^(- 1+(- 44)) - 45
2 and 22
^(2* 22) 44
^(2+22) 24
- 2 and - 22
^(- 2* (- 22)) 44
^(- 2+(- 22)) - 24
4 and 11
^(4* 11) 44
^(4+11) 15
- 4 and - 11
^(- 4* (-11)) 44
^(- 4+(- 11)) - 15
The integers whose product is 44 and whose sum is 15 are 4 and 11.
44+15h+h^2 ⇔ (h+4)(h+11)
Let's use a graphing calculator to confirm our answer. To do so, we will graph the related functions in the same coordinate plane. Note that in the calculator we will use the variable x instead of h.
We see that only one graph appears. This means that both graphs coincide. Therefore, the expression has been factored correctly.
