Final answer:
To divide the polynomial (x²-24) by (x-5), we can use long division. The quotient is (x - 5) and the remainder is -49.
Step-by-step explanation:
Dividing Polynomials
To divide the polynomial (x²-24) by (x-5), we can use long division. First, we divide the first term of the polynomial (x²) by the first term of the divisor (x). This gives us x as the quotient. Then, we multiply the divisor (x-5) by the quotient (x), which gives us x(x-5) = x² - 5x. Now, we subtract this result from the original polynomial (x²-24). The result is -5x - 24.
Next, we bring down the next term from the dividend, which is -24. We divide -5x by x, which gives us -5 as the quotient. Then, we multiply the divisor (x-5) by the quotient (-5), which gives us -5(x-5) = -5x + 25. We subtract this result from the previous remainder (-5x - 24). The result is -49.
Since we have no more terms to bring down and the remainder (-49) is of lower degree than the divisor, we can stop here. The final quotient is (x - 5) and the remainder is -49. Therefore, the division can be written as:
(x²-24) ÷ (x - 5) = (x - 5) + (-49)/(x - 5)
Learn more about Dividing polynomials