To factor the quadratic expression, we will start by identifying the values of a, b, and c.
n^2-2n-35 ⇔ 1n^2+( - 2)n+( - 35)
For our expression, we have that a= 1, b= - 2, and c= - 35.
To factor a quadratic expression with leading coefficient a= 1, we need to find two factors of c= - 35 whose sum is b= - 2. Since - 35 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 - 35
^(1* (- 35)) - 35
1+(- 35) - 34
- 1 and 35
^(- 1* 35) - 35
^(- 1+35) 34
5 and - 7
^(5* (- 7)) - 35
^(5+(- 7)) - 2
- 5 and 7
^(- 5* 7) - 35
^(- 5+7) 2
The integers whose product is - 35 and whose sum is - 2 are - 7 and 5.
n^2-2n-35 ⇔ (n-7)(n+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. 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.
