Divide: Left Parenthesis x-squared minus 10 x plus 30 Right Parenthesis divided by Left Parenthesis x minus 5 Right Parenthesis.
A. x minus 10 minus 6
B. x minus 5 minus Start Fraction 5 over x minus 5 End Fraction
C. x minus 10 minus Start Fraction 30 over x minus 5 End Fraction
D. x minus 5 plus Start Fraction 5 over x minus 5 End Fraction
The first step in dividing polynomials is to check if the numerator can be factored. In this case, we can factor the numerator as follows:
x² - 10x + 30 = (x - 5)(x - 6)
So the expression simplifies to:
(x - 5)(x - 6) / (x - 5)
We can then cancel out the common factor of (x - 5), and we are left with:
x - 6
Therefore, the answer is (A) x - 10 - 6.