Question

12.On dividing 3.x3 – 2x2 + 5x + 5 by the polynomial p(x), the quotient and remainder are x2 - x +2 and– 7 respectively. Find p(x)?(CBSE 2013)

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Answer 1

Answer:

Hope this will help you

Answer 2

given : polynomial = 3x³-2x²+5x-5

quotient = x²-x+2

remainder = -7

solution :

using the division algorithm

dividend = divisor ×quotient + remainder

3x³-2x²+5x-5  = p(x) × (x²-x+2) +  (-7)

3x³-2x²+5x-5 +7 = p(x) × (x²-x+2)

3x³-2x²+5x+2= p(x) × (x²-x+2)

p(x) = $\frac{3x^3-2x^2+5x+2 }{x^2-x+2}$

thus ,

P(x) = 3x+1

The divison is shown in the below attachment

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