To factor the quadratic expression, we will start by identifying the values of a, b, and c.
m^2-15m+50
⇕
1m^2+( - 15)m+ 50
For our expression, we have that a= 1, b= - 15, and c= 50.
To factor a quadratic expression with leading coefficient a= 1, we need to find two factors of c= 50 whose sum is b= - 15. Since 50 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 50
^(1* 50) 50
1+50 51
- 1 and - 50
^(- 1* (- 50)) 50
^(- 1+(- 50)) - 51
2 and 25
^(2* 25) 50
^(2+25) 27
- 2 and - 25
^(- 2* (- 25)) 50
^(- 2+(- 25)) - 27
5 and 10
^(5* 10) 50
^(5+10) 15
- 5 and - 10
^(- 5* (- 10)) 50
^(- 5+ (- 10)) - 15
The integers whose product is 50 and whose sum is - 15 are - 5 and -10.
m^2-15m+50 ⇔ (m-5)(m-10)
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 m.
We see that only one graph appears. This means that both graphs coincide. Therefore, the expression has been factored correctly.
