To factor the quadratic expression, we will start by identifying the values of a, b, and c.
n^2+4n-21 ⇔ 1n^2+ 4n+( - 21)
For our expression, we have that a= 1, b= 4, and c= - 21.
To factor a quadratic expression with leading coefficient a= 1, we need to find two factors of c= - 21 whose sum is b= 4. Since - 21 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 - 21
^(1* (- 21)) - 21
1+(- 21) - 20
- 1 and 21
^(- 1* 21) - 21
^(- 1+21) 20
3 and - 7
^(3* (- 7)) - 21
^(3+(- 7)) - 4
- 3 and 7
^(- 3* 7) - 21
^(- 3+7) 4
The integers whose product is - 21 and whose sum is 4 are 7 and - 3.
n^2+4n-21 ⇔ (n+7)(n-3)
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 n.
We see that only one graph appears. This means that both graphs coincide. Therefore, the expression has been factored correctly.
