Answer:
a = 1
Explanation:
We have the expression:
12x² + ax - 20
3x + 4 is a factor. Therefore:
12x² + ax - 20 = (3x · 4x) + ax + (4 · (-5))
12x² + ax - 20 = (3x + 4)(4x - 5)
(3x + 4)(4x - 5) = (3x)(4x) + (3x)(-5) + (4)(4x) + (4)(-5)
= 12x² - 15x + 16x - 20 = 12x² + x - 20
a = 1
Other method:
12x² + ax - 20 = (3x + 4)(bx + c)
12x² + ax - 20 = (3x)(bx) + (3x)(c) + (4)(bx) + (4)(c)
12x² + ax - 20 = 3bx² + 3cx + 4bx + 4c
12x² + ax - 20 = 3b² + (3c + 4b)x + 4c
therefore
3b = 12
a = 3c + 4b
4c = -20
3b = 12 ⇒ b = 4
4c = -20 ⇒ c = -5
substitute to a:
a = 3 · (-5) + 4 · 4
a = -15 + 16
a = 1