Given f(x) = 2x^2+ kx – 9, and the remainder when f(x) is divided by x + 6 is 57, then what is the value of k?

Given:

The function is

The remainder when f(x) is divided by x+6 is 57.

To find:

The value of k.

Solution:

According to the remainder theorem, if a polynomial function f(x) is divided by (x-a), then f(a) is the remainder.

The remainder when f(x) is divided by x+6 is 57.

Using remainder theorem, we get f(-6)=57.

Putting x=-6 in the given function.

On further simplification, we get

Therefore, the value of k is 1.

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2

to determine the unit cost your would divide the total cost by the number sold.

7 bagels for $4.41       $4.41/7 = $.63 each at fresh side

5 bagels for $3.60         $3.60/5 = $.72 each at value mart