When divided by x-3 the polynomials x 3-px 2+x+6

If (x – 3) divides f(x) = x3 – px2 + x + 6, then,
Remainder = f(3) = 33 – p(3)2 + 3 + 6 = 36 – 9p
If (x – 3) divides g(x) = 2x3 – x2 – (p + 3) x – 6, then
Remainder = g(3) = 2(3)3 – (3)2 – (p + 3) (3) – 6 = 30 – 3p
Now, f(3) = g(3)
⇒ 36 – 9p = 30 – 3p
⇒ -6p = -6
⇒  p = 1

If (x – 3) divides f(x) = x3 – px2 + x + 6, then
Remainder = f(3) = 33 – p(3)2 + 3 + 6 = 36 – 9p
If (x−3) divides g(x) = 2x3 – x2 − (p + 3)x – 6, then
Remainder = g(3) = 3(3)3 – 32 − (p + 3)(3) – 6 = 30 - 3p

Now f(3) = g(3)

⇒ 36 – 9p = 30 − 3p

⇒ −6p = −6

⇒ p = 1

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