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Remainder Theorem

The polynomia...

Question

The polynomials p(x) = x³ + 2x² – 5x -7 and q(x) = x³ + x² – 12x + 6, when divided by (x + 1) and (x - 2) respectively give the remainders R₁ and R₂. Find 2R₁+ R₂ .

A

2

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B

4

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C

8

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D

-8

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Solution

The correct option is D
-8

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Similar questions

Let r1 and r2 be the remainders when the polynomials

p(x)= x3+x2-5kx-7 and q(x)=x3+kx2-12x+6

are divided by x+1 and x-2 respectively.

Find the value of k if 2r1-r2=10

R_{1}

R_{2}

are the remainder when the polynomials

x^{3} + 2 x^{2} - 5 a x - 7

x^{3} + a x^{2} - 12 x + 6

x + 1

x - 2

respectively. If

2 R_{1} + R_{2} = 6

, find the value of

a

.

Q. Two polynomials

(2 x^{3} + x^{2} - 6 a x + 7)

(x^{3} + 2 a x^{2} - 12 x + 4)

(x + 1)

(x - 1)

respectively. If

R_{1}

R_{2}

are the remainders and

2 R_{1} + 3 R_{2} = 27

, find the value of

a

Q. The polynomials

a x^{3} + 3 x^{2} - 3

2 x^{3} - 5 x + a

when divided by (x -4) leaves remainders

R_{1},

R_{2}

respectively then value of 'a' if

2 R_{1} - R_{2} = 0.

Q. The polynomials

a x^{3} + 3 x^{2} - 3

2 x^{3} - 5 x + a

when divided by (x - 4) leaves remainder

R_{1}

R_{2}

2 R_{1} - R_{2} = 0

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