x=-3,-2,3/2 (option C)
Explanation:
p(x) = (x+2) (2x²+3x-9)
to get the zeros, we equatoe the factors with zero
x + 2 = 0
x = -2
2x²+3x-9 = 0
we factorise using factorisation method
a = 2, b= 3, c = -9
The product of a and c = -18
two factors of -18 that sum up to 3 but their product gives -18 is 6 and -3
2x²+6x-3x-9 = 0
2x(x + 3) -3(x + 3) = 0
(2x-3)(x+3) = 0
2x-3 = 0 or x+3 = 0
2x = 3 or x = -3
x = 3/2 or x = -3
Hence, the factors of p(x) = (x+2) (2x²+3x-9) are x = -2, 3/2, -3
The correct option: x=-3,-2,3/2 (option C)
