How do you use the remainder theorem to find the remainder for each division #(x^2+2x-15)div(x-3)#?

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Answer 1 · 2016-11-26T18:57:26

The remainder #=0#

When we divide a polynomial #f(x)# by #(x-a)#

we get, #f(x)=(x-a)q(x)+r#

If #x=a#

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

So, #f(a)=r#

Here, #f(x)=x^2+2x-15# is divided by #(x-3)#

#f(3)=3^2+2*3-15=9+6-15=0#

Remainder #=0#

#f(x)# is divisible by #(x-3)#

#(x^2+2x-15)/(x-3)=(cancel(x-3)(x+5))/cancel(x-3)#