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

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Answer 1 · 2016-11-07T00:04:51

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!

Answer 2 · 2016-11-07T00:08:46

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.

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