Answer: 5x + 15
Step-by-step explanation:
Divide (x² + 5) into (x³ + 4x² + 5) to see what is needed to make a remainder of zero.
Let k represent the unknown number.
x + 4
x² + 5 ) x³ + 4x² + 0x + 5+k
- (x³ + 5x)
4x² - 5x + 5+k
- (4x² + 20)
In order to have a remainder of zero, 4x² -5x + 5 + k must equal 4x² + 20
Solve for k:
4x² -5x + 5 + k = 4x² + 20
-5x + 5 + k = 20 subtracted 4x² from both sides
5 + k = 5x + 20 added 5x to both sides
k = 5x + 15 subtracted 5 from both sides
