# How do you use the remainder theorem to evaluate #f(x)=x^3+x^2-5x-6# at x=2?

##### 1 Answer

# f(2) = -4 #

#### Explanation:

We use the remainder theorem to establish what the remainder is when we divide a polynomial function by a linear factor.

Here we are given a function and asked to evaluate the value of the function at a given value, so we can just evaluate it:

We have:

# f(x) =x^3+x^2-5x-6 #

And so, when

# f(2) =8+4-10-6 = -4 #

We can also use the remainder theorem to establish a value of

So, let us divide the given polynomial,

# {: ( , , , , x^2 , + , 3x , +, 1 , ), ( , ,"----", "----", "----", "----", "----", "----", "----" , ), (x-2, ")" , x^3, +,x^2, -,5x,-,6, ), ( , , x^3, -, 2x^2, , , , , - ), ( , , , ,"----", "----", "----", "----", "----", ), ( , , , , 3x^2, -, 5x, -, 6, ), ( , , , , 3x^2, -, 6x, , , - ), ( , , , , , ,"----", "----", "----" , ), ( , , , , , , x, -, 6, ), ( , , , , , , x, -, 2, -), ( , , , , , , , "----", "----" , ), ( , , , , , , , -, 4, ) :} #

And we have remainder