Question

X^2-x-12 factor completely

Answer 1

Use the sum-product pattern

2
−

−
1
2
x
2
−
x
−
12
x2−x−12

2
+
3

−
4

−
1
2
x
2
+
3
x
−
4
x
−
12
x2+3x−4x−12
2
Common factor from the two pairs

2
+
3

−
4

−
1
2
x
2
+
3
x
−
4
x
−
12
x2+3x−4x−12

(

+
3
)
−
4
(

+
3
)
x
(
x
+
3
)
−
4
(
x
+
3
)
x(x+3)−4(x+3)
3
Rewrite in factored form

(

+
3
)
−
4(+3)x
(x+3)−4(x+3)
x(x+3)−4(x+3)
(−4)(+3)
(x−4)(x+3)
(x−4)(x+3)