Question

Synth Divide. Check your answer by multiplication. (x²-4x-13)/(x-3)

Answer 1

To divide the expression (x²-4x-13)/(x-3), perform long division by following several steps. The quotient is x-1 with a remainder of -10. Multiplying the divisor and the quotient, adding the remainder, should result in the original dividend.

Step-by-step explanation:

To divide the given expression (x²-4x-13)/(x-3), we need to perform long division. Here are the steps:

1. Divide x² by x to get x.
2. Multiply x by (x-3) to get x²-3x.
3. Subtract x²-3x from x²-4x to get -x.
4. Bring down the -13 to get -13x.
5. Divide -x by x to get -1.
6. Multiply -1 by (x-3) to get -x+3.
7. Subtract -x+3 from -13x to get -10.
8. Since there are no more terms to bring down, the division is complete.

Therefore, the division of the given expressions is x-1 with a remainder of -10. To check this answer, we can multiply the divisor (x-3) by the quotient (x-1) and add the remainder (-10), which should give us the original dividend (x²-4x-13).

(x-3)(x-1)-10 = x²-4x-13. Hence, the answer is correct.

Learn more about Dividing Algebraic Expressions