Answer
To solve the equation, factor x
2
−7x+12 using formula x
2
+(a+b)x+ab=(x+a)(x+b). To find a and b, set up a system to be solved.
a+b=−7
ab=12
Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 12.
−1,−12
−2,−6
−3,−4
Calculate the sum for each pair.
−1−12=−13
−2−6=−8
−3−4=−7
The solution is the pair that gives sum −7.
a=−4
b=−3
Rewrite factored expression (x+a)(x+b) using the obtained values.
(x−4)(x−3)
To find equation solutions, solve x−4=0 and x−3=0.
x=4
x=3
Step-by-step explanation:
