To factor the quadratic expression, we will start by identifying the values of a, b, and c.
x^2+3x-18 ⇔ 1x^2+ 3x+( - 18)
For our expression, we have that a= 1, b= 3, and c= - 18.
To factor a quadratic expression with leading coefficient a= 1, we need to find two factors of c= - 18 whose sum is b= 3.
Since - 18 is a negative number, we will only consider factors with opposite signs — one positive and one negative — so that their product is negative.
Factor Pair
Product
Sum
1 and - 18
^(1* (- 18)) - 18
^(1+(- 18)) - 17
- 1 and 18
^(- 1* 18) - 18
^(- 1+18) 17
2 and - 9
^(2* (- 9)) - 18
^(2+(- 9)) - 7
- 2 and 9
^(- 2* 9) - 18
^(- 2+9) 7
3 and - 6
^(3* (- 6)) - 18
^(3+(- 6)) - 3
- 3 and 6
^(- 3 * 6) - 18
^(- 3+6) 3
The integers whose product is - 18 and whose sum is - 5 are - 3 and 6.
x^2+3x-18 ⇔ (x-3)(x+6)
Let's use a graphing calculator to confirm our answer. To do so, we will graph the related functions in the same coordinate plane.
We see that only one graph appears. This means that both graphs coincide. Therefore, the expression has been factored correctly.
