Question

The polynomial function f(x)=X^3-2x^2+ax-8 has (x-2) as one of its factors. What would be the remainder when f(x) is divided by (x – 4)?
A: -120
B: -56
C. 4.
D. 40 ​

Answer 1

Answer:

option A is the answer.......

Answer 2

The remainder is 40 if the polynomial function f(x) = x³-2x²+ax-8 has (x-2) value of a is 4 option (D) is correct.

What is polynomial?

Polynomial is the combination of variables and constants in a systematic manner with "n" number of power in ascending or descending order.

$\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n$

We have a polynomial function:

$\rm f(x)= x^3-2x^2+ax-8$

(x-2) is a factor of the above polynomial

To get the value of a put x = 2 in the polynomial and equate to zero.

$\rm 2^3-2(2)^2+a(2)-8=0$

$\rm a = 4$

$\rm f(x)= x^3-2x^2+4x-8$

From the remainder theorem:

Put x = 4 in the polynomial to get the remainder

$\rm R =f(4)= (4)^3-2(4)^2+4(4)-8$

$\rm R = 64-32+16-8\\\\R = 40$

Thus, the remainder is 40 if the polynomial function f(x)=x³-2x²+ax-8 has(x-2) value of a is 4 option (D) is correct.

Learn more about Polynomial here:

brainly.com/question/17822016

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