Answer to Question #42513 in Calculus for shasha

Question

Find the remainder when f(x) is divided by (x - k)

f(x) = 4x3 - 6x2 + 3x + 1; k= -2

-3

-61

26

-49

show work please and explanation

Answer 1

f(x)/(x+2) = (4x3 - 6x2 + 3x + 1)/(x+2)
4x3 - 6x2 + 3x + 1|x+2
4x3+8x2 |4x^2-14x+31
-14x2+3x
-14x2-28x
31x+1
31x+62
-61
And we get
f(x)/(x+2) = (4x3 - 6x2 + 3x + 1)/(x+2) = (4x2-14x+31)(x+2) - 61
remainder is -61