How do you find "a" if the remainder is a when x^3 + 3x^2 - ax + 3 is divided by x - 2?

Answer 1

Use polynomial long division:

(x-2) | x^3 + 3x^2 - ax + 3

x^3 - 2 x^2

_________

0 + 5 x^2 - ax

5 x^2 - 10 x

__________

0 - (a - 10) x + 3

(a - 10) x + -2(a-10)

________________

0 + -17 + 2 a

remainder: ----------------------------^ (2a - 17)