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Looking at the options, we can deduce that (x - 5) given in the denominator of H gets canceled.BTGmoderatorDC wrote:If H = [(x^3) - 6(x^2) - x + 30] / (x-5)and x ≠5, then H is equivalent to which of the following?
A. (x^2) - x - 6
B. (x^3) + 3(x^2) + 3x
C. (x^3) - 25
D. (x^3) - 5(x^2) - 3x
E. (x^2) + x + 10
OA A
Source: Manhattan Prep
Let x=0, with the result that H = 30/-5 = -6.BTGmoderatorDC wrote:If H = [(x^3) - 6(x^2) - x + 30] / (x-5)and x ≠5, then H is equivalent to which of the following?
A. (x^2) - x - 6
B. (x^3) + 3(x^2) + 3x
C. (x^3) - 25
D. (x^3) - 5(x^2) - 3x
E. (x^2) + x + 10
We see that the numerator of H, x^3 - 6x^2 - x + 30, is not a polynomial that can be easily factored. However, since x^3/x (the first term of numerator divided by the first term of the denominator) is x^2 and 30/(-5) (the constant term of numerator divided by the constant term of the denominator) is -6, we see that if H can be simplified, the answer must be choice A: x^2 - x - 6. Now let's verify it is the case by multiplying it by (x - 5) to see if the product is x^3 - 6x^2 - x + 30.BTGmoderatorDC wrote:If H = [(x^3) - 6(x^2) - x + 30] / (x-5)and x ≠5, then H is equivalent to which of the following?
A. (x^2) - x - 6
B. (x^3) + 3(x^2) + 3x
C. (x^3) - 25
D. (x^3) - 5(x^2) - 3x
E. (x^2) + x + 10
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