Question

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​

Answer 1

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

Answer 2

Answer:

a= -3

now the remainder of first polynomial is 54+9a = 54+9(-3)=54-27= 27

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