Question

If the polynomials (2x3 + ax2 + 3x – 5) and (x3 + x2 – 2x + a) leave the same remainder when divided by (x – 2), find the value of a. Also , find the remainder in each case.

Answer 1

Step-by-step explanation:

Hi there!

Let the given polynomials be f(x) and g(x).

ATQ, 

When f(x) and g(x) are divided by (x-2) they leave the same remainder.

I.e (x-2) is a factor of f(x) and g(x). It means 2 is the zero of f(x) and g(x)

So that,

f(2) = g(2)

2x³+ax²+3x-5 = x³+x²-4x+a

2(2)³+a(2)²+3(2)-5 = 2³+2²-4(2)+a

2(8)+a(4)+6-5 = 8+4-8+a

16+4a+1 = 4+a

17+4a = 4+a

4a-a = 4-17

3a = -13

a = -13/3.

Hope helped!

:)

Answer 2

Step-by-step explanation:

Just substitute the value of x with 2 in both the cases and then it is already given that their remainders are same so write the value of A(x) (after putting x=2 in that equation) = B(x) (after substituting). And you get the answer. You can also see the picture which I have posted.