How do you use the remainder theorem to find the remainder for the division #(10x^3-11x^2-47x+30)div(x+2)#?

2 Answers
Nov 7, 2016

The remainder states that when any polynomial #f(x)# is divided by #x - a#, the remainder is #f(a)#.

So, Letting #f(x) = 10x^3 - 11x^2 - 47x + 30#, we have:

#f(-2) = 10(-2)^3 - 11(-2)^2 - 47(-2) + 30#

#f(-2) = 10(-8) - 11(4) + 94 + 30#

#f(-2) = -80 - 44 + 94 + 30#

#f(-2)= 0#

The remainder is #0#. In other words, #x + 2# is a factor of #10x^3 - 11x^2 - 47x +30#.

Hopefully this helps!

Nov 7, 2016

This expression has a remainder of zero.
#(10x^3-11x^2-47x+30)/(x+2)# is equal to #(10x^2-31x+15)#, with no remainder.