Answer:
5x^2 + 7x + 30 + 102/x-3
Step-by-step explanation:
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x-3| 5x^3 - 8x^2 + 9x + 12
First you would want to set it up as either long polynomial division or using synthetic division. Whichever one is easier for you. However, I am going to use long polynomial division since you might not be familiar with synthetic division just yet.
_<u>5x^2</u>_____________
x-3| 5x^3 - 8x^2 + 9x + 12 Because 5x^3 divided by x gives you 5x^2
<u>- (5x^3 - 15x^2)</u>______ and -3 times 5x^2 gives you -15x^2
0 + 7x^2 +9x But since the negative is outside the parentheses then you distribute it turning he -15x^2 it into +15x then adding it to the -8x^2 above it thus giving you 7x^2. Afterwards bring down the 9x.
A negative times a negative is a positive (just as a reminder)
Next,
_<u>5x^2+7x</u>_________
x-3| 5x^3 - 8x^2 + 9x + 12
<u>- (5x^3 - 15x^2)</u>______ 7x^2 divided by x gives you 7x
0 + 7x^2 + 9x
<u>- (7x^2 - 21x)</u>___ and 7x times -3 gives you -21x
0 + 30x +12 you distribute the negative in the parentheses again.
Then,
_<u>5x^2 +7x +30</u>____
x-3| 5x^3 - 8x^2 + 9x + 12
<u>- (5x^3 - 15x^2</u>)______
0 + 7x^2 + 9x
<u> - (7x^2 - 21x)</u>___
0 + 30x + 12 30x divided by x gives you 30.
<u>- (30x - 90)</u> Distribute the negative again.
0 + 102 102 is the remainder.
When writing remainders in long polynomial equations, it is expressed by writing the remainder over the divisor. Which is 102/x-3.
So the answer is 5x^2 + 7x + 30 + 102/x-3.
