polynomial

If x³ – 6x² + px + q is exactly divisible (x² – 3x + 2), then find the value of p and q

Answer:

Since, x³ – 6x² + px + q is exactly divisible (x² – 3x + 2), let (x + a) be the quotient.

Therefore, (x² – 3x + 2) (x + a) = x³ + (a – 3) x² + (2 – 3a) x + 2a = x³ – 6x² + px + q

Comparing the coefficients we get

(a – 3) = -6, or a = -3

2 – 3a = p, or p = 2 – 3*-3 = 11

2a = q, or q = 2* -3 = -6