To divide the polynomial x²-5x-2, use polynomial long division. The quotient is x-3 and the remainder is -8. The answer is (x-3) -8/(x-2).
To divide the polynomial x²-5x-2, we need to use polynomial long division.
Divide the first term of the numerator, x², by the first term of the denominator, x. This gives us x.
Multiply the denominator, x-2, by the quotient from step 1, which is x, to get x(x-2) = x²-2x.
Subtract the product from step 2 from the numerator, x²-5x-2, to get a new numerator, -3x-2.
Repeat steps 1-3 with the new numerator, -3x-2.
Divide the first term of the new numerator, -3x, by the first term of the denominator, x. This gives us -3.
Multiply the denominator, x-2, by the quotient from step 5, which is -3, to get -3(x-2) = -3x+6.
Subtract the product from step 6 from the new numerator, -3x-2, to get a new numerator, -8.
We cannot divide -8 by x-2 anymore, so our final division is complete.
The quotient of the division is x-3, and the remainder is -8.
Therefore, the division of the polynomial x²-5x-2 is x-3 with a remainder of -8.
The answer can be written in the form p(x) + k/(x-2), where p(x) represents the quotient x-3 and k represents the remainder -8. So, the final answer is (x-3) -8/(x-2).