Question

If 2x-3 is a factor of the polynomial 2x³-9x²+x+p, find the value of p. Hence, find all the factors of the polynomial.

Answer 1

2x-3 is a factor of 2x³-9x²+x+p hence on division remainder is 0 for p = 12 
factors = (2x-3)(x-4)(x+1)

Answer 2

When we divide 2x³-9x²+x+p by 2x-3, we get a remainder as p-12.
p-12=0 ⇒ p=12
So the value of p is 12.
Now, we got the quotient as x²-3x-4.
x²-3x-4
=x²-4x+x-4
=x(x-4)+1(x-4)
=(x+1) (x-4)
So the factors of p(x) are (2x-3), (x+1) and (x-4).