Divide x³+2x³-4x+3 by x-2
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Step-by-step explanation:
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harinivarshini81
harinivarshini81
06.08.2019
Math
Secondary School
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if two polynomials 2x³+ax²+4x-12 and x³+x²-2x+a leave the same remainder when divided by (x-3), find the value of a and also find the remainder
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Step-by-step explanation:
when p(x)= 2x^3 +ax^2+4x-12 is divided by (x-3).
then X=3 .
so, p(3)= 2(3)^3+a(3)^2+4(3)-12.
54+9a+12-12.
54+9a .........(i).
when p(x)= x^3+x^2 -2x+a is divided by (x-3).
then X=3.
so, p(3)=(3)^3+(3)^2-2(3)+a.
27+9-6+a.
30+a........(ii).
these two polynomial leaves the same remainder when divided by (x-3) .
so, 54+9a=30+a.
9a-a=30-54.
8a =-24.
hence , a= -3.
now the remainder of first polynomial is 54+9a = 54+9(-3)=54-27= 27
Given,
x³+2x³-4x+3 by (x-2)
3x³-4x+3 by (x-2)