math for Algebra one?

Question

when x^3 + k is divided by x+2, the remainder is known to be -15. Find the numberical value of k. SHOW WORK PLEASE

Answer 1

The solution is determined by dividing it out as if it were long division:

x^3 - k is the numerator

x + 2 is the denominator

The term with highest degree of x in the numerator (x^3) divided by the term with highest degree of x in the denominator is x^2, so that is the first part of the quotient.

Now subtract x^2(x+2) from the numerator...

x^3 + k - (x^2(x+2)) =
x^3 + k - x^3 - 2x^2 =
-2x^2 + k

The term with highest degree of x in what is left of the numerator (-2x^2) divided by the term with highest degree of x in the denominator is -2x, so that is the second part of the quotient.

Now subtract -2x(x+2) from the numerator...

-2x^2 + k - (-2x(x+2)) =
-2x^2 + k +2x^2 + 4x =
4x + k

The term with highest degree of x in what is left of the numerator (4x) divided by the term with highest degree of x in the denominator is 4, so that is the final part of the quotient.

Now subtract 4(x+2) from the numerator...

4x + k - (4(x+2)) =
4x + k -4x - 8 =
k - 8

We end up with a remainder of k-8. However, we were given that the remainder is -15, so...

k - 8 = -15
k = -7

Answer 2

( x^3 + k ) / ( x + 2 ) = x^2 - 2x + 4 + ( k - 8 )
now if reminder is -15; k - 8 equals -15
k = -15 + 8 = -7
Workschem:
1st step:
( x^2 )( x^2 ) = x^3 + 2x^2
x^3 + k - ( x^3 + 2x^2 ) = - 2x^2 + k
2nd step:
( x+2 )( -2x ) = - 2x^2 - 4x
now difference with
-2x^2 + k - ( - 2x^2 - 4x ) = 4x + k
3rd step:
4( x + 2 ) = 4x + 8
finally:
4x + k - ( 4x + 8 ) = k - 8
and then if
k - 8 = - 15
k = - 7
as a result