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Question

The polynomials ax​​​​​ax3​​- 3x2+4 and 2x3-5x+a when divided by x-2 leave the remainder p and q respectively.If p-2q=4 , find a

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Solution

p(x)=ax^3-3x^2+4

g(x)=2x^3-5x+a ..

factor of g(x) and p(x) are x-2

p(2)= 8a-12+4=p [Remainder thm.]

= 8a-8=p

g(2)=16-10+a=q

=6+a=q

p-2q=4

8a-8-2(6+a)=4

8a-8-12-2a=4

6a-20=4

6a=24

a=24/6=4

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