How do you find the remainder when 1.f(x)=x^3+2x^2-6x+8; x+41.f(x)=x3+2x26x+8;x+4?

1 Answer
Mar 22, 2018

The remainder is 00

Explanation:

The remainder theorem tell us that if we divide a polynomial f(x)f(x) by a linear factor (x-a)(xa) then the remainder is f(a)f(a)

Thus the remainder we seek for:

f(x) = x^3+2x^2-6x+8 f(x)=x3+2x26x+8

divided by (x+4)(x+4) is given by:

f(-4) = (-4)^3+ 2(-4)^2-6(-4)+8 f(4)=(4)3+2(4)26(4)+8
\ \ \ \ \ \ \ \ \ \ \ = -64+ 32+24+8
\ \ \ \ \ \ \ \ \ \ \ = 0

And we can conclude that x+4 is a factor