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# 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’. - ICSE Class 10 - Mathematics

ConceptFactorising a Polynomial Completely After Obtaining One Factor by Factor Theorem

#### Question

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’.

#### Solution

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

Is there an error in this question or solution?

#### APPEARS IN

2009-2010 (March) (with solutions)
Question 4.1 | 3.00 marks
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: Factorising a Polynomial Completely After Obtaining One Factor by Factor Theorem.
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