Question

The polynomials (ax^3 + 3x^2 − 3) and (2x^2 − 5x + a) when divided by (x – 4) leave
the same remainder. Find the value of a.

Answer 1

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Answer 2

Given polynomial p(x)=ax3+3x2−13and 2x2−5x+a is divided by x-2 get same remainder

Then x-2=0 or x=2

p(x)=ax3+3x2−13

Replace x by 2 we get 

p(2)=a(2)3+3(2)2−13

⇒p(2)=8a+12−13

⇒p(2)=8a−1

2x2−5x+a

Replace x by 2 we get

q(2)=2(2)3−5(2)+a

⇒q(2)=16−10+a

⇒q(2)=6+a

Given remainder is same 

∴8a−1=6+a

⇒8a−1+1−a=6+a+1−a

⇒7a=7

a=1