Question

if two polynomials 2x^3+ax^2+4x-12 and x^3+x^2-2x+a leave the same remainder when divided by (x-3) find the value of a and also find the remainder​



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Answer 1

Answer:

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Answer 2

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Let p(x)=2x^3 +ax ^2 +4x−12,

q(x)=x 3^ +x ^2 −2x+a.

When p(x) is divided by (x-3) the remainder is p(3). Now,

p(3)=2(3) ^3+a(3) ^2 +4(3)−12

->2(27)+a(9)+12−12

54+9a ....(1)

When q(x) is divided by (x-3) the remainder is q(3). Now,

q(3)=2(3) ^3 +(3) ^2+2(3)+a

->(27)+(9)−6+a

30+a ...(2)

Given that p(3)=q(3). That is,

54+9a=30+a (By (1) and (2))

9a−a=30−54

8a=−24

∴a=−24/8= -3

Substituting a=-3 in p(3), we get,

p(3)=54+9(−3)=54−27=27

∴ The remainder is 27.

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