# How do you use the remainder theorem to evaluate #f(x)=x^5-47x^3-16x^2+8x+52# at x=7?

##### 1 Answer

Jan 16, 2017

#### Explanation:

Remainder theorem states that if a polynomial

Hence to evaluate

Now,

#=x^4(x-7)+7x^3(x-7)+2x^2(x-7)-2x(x-7)-6(x-7)+10#

#=(x^4+7x^3+2x^2-2x-6)(x-7)+10#

As such the remainder on dividing

hence

**Check**

#=16807-16121-784+56+52=10#