Divide until the degree of the divisor is greater than the degree of the dividend.
A
Practice makes perfect
We are given the following expression.
(x^2+3x-9)(4-x)^(- 1)
First, we need to remove the negative power. We will do this using the Negative Exponent Rule, which states that negative exponents in the numerator get moved to the denominator and become positive exponents.
x^2+3x-9/(4-x)^1
Now the denominator is raised to the power of 1, which does not change the denominator. We do not have to write the exponent of 1.
x^2+3x-9/4-x
Before we divide, we can also rewrite the denominator as - x+4. Now let's simplify the fraction using polynomial long division.
l r - x + 4 & |l x^2+3x-9
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Divide
x^2/- x= - x
r - x r - x + 4 & |l x^2 + 3x - 9
Multiply term by divisor
r - x rl - x+4 & |l x^2 + 3x - 9 & x^2 - 4x
Subtract down
r - x r - x+4 & |l 7x - 9
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Divide
7x/- x= - 7
r - x - 7 r - x+4 & |l 7x - 9
Multiply term by divisor
r- x - 7 rl - x+4 & |l 7x - 9 & 7x-28
Subtract down
r - x - 7 r - x+4 & |l 19
The quotient is - x - 7 with a remainder of 19. Therefore, the exact value of the above fraction is equal to - x - 7 plus the remainder 19 divided by - x+4, or 4-x.
x^2+3x-9/4-x=- x - 7 + 19/4-x
The answer is A.
Showing Our Work
Long division by hand...
When doing long division by hand, it looks a bit different than how we have it in this solution. Here is how yours should look when you are writing it in your notebook.
