How do you use the remainder theorem to determine the remainder when the polynomial #8x^3+4x^2-19# is divided by #x+2#?

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Answer 1 · 2016-12-08T08:25:13

The remainder is #=-67#

If we have a polynomial #f(x)# and we divide by #(x-c)#

Then,

#f(x)=(x-c)q(x)+r(x)#

If #x=c#

We have, #f(c)=O+r#

#r# is the remainder

That's the remainder theorem

Here, #f(x)=8x^3+4x^2-19#

and #c=-2#

So, #f(-2)=-8*8+4*4-19=-64+16-19=-67#