Question

Find the values of p and q so that (x - 2) and (x - 3) are the factors of
the polynomial f(x) = 5x^3 + 6x^2 - px + q.​

Answer 1

Since x-2 is a factor of f(x)

f(2)=0

5*2³+6*2²-p*2+q=0

40+24-2p+q=0

q=2p-64

Again, x-3 is also a factor of f(x). so,

f(3)=0

5*3³+6*3²-3*p+q=0

135+54-3p+2p-64=0

125-p=0

p=125

Again,

q=2*125-64=186