#### Question

When divided by x – 3 the polynomials x^{3} – px^{2} + x + 6 and 2x^{3} – x^{2} – (p + 3) x – 6 leave the same remainder. Find the value of ‘p’.

#### Solution

If (x – 3) divides f(x) = x^{3} – px^{2} + x + 6, then,

Remainder = f(3) = 3^{3} – p(3)^{2} + 3 + 6 = 36 – 9p

If (x – 3) divides g(x) = 2x^{3} – x^{2} – (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

Is there an error in this question or solution?

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Solution When divided by x – 3 the polynomials x3 – px2 + x + 6 and 2x3 – x2 – (p + 3) x – 6 leave the same remainder. Find the value of ‘p’. Concept: Remainder Theorem.

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