Question

Divide 2x⁵-x⁴-26x³ 13x² 72x-36 by 2x-1.

A) Quotient: 2x⁴+x³-25x²-12x+36, Remainder: 0
B) Quotient: x⁵-x⁴-26x³-13x²-72x+36, Remainder: 0
C) Quotient: x⁴+x³-25x²-12x+36, Remainder: 0
D) Quotient: 2x⁵-x⁴-26x³-13x²-72x+36, Remainder: 0

Answer 1

To divide 2x⁵ - x⁴ - 26x³ + 13x² + 72x - 36 by 2x - 1, we can use long division. The quotient is x⁴ - 13x² + 36 and the remainder is 0.

Step-by-step explanation:

To divide the expression 2x⁵ - x⁴ - 26x³ + 13x² + 72x - 36 by 2x - 1, we can use long division.

1. First, divide the highest degree term of the dividend, which is 2x⁵, by the highest degree term of the divisor, which is 2x. This gives us x⁴.
2. Multiply the divisor, 2x - 1, by the quotient, x⁴. This gives us 2x⁵ - x⁴.
3. Subtract this product from the original dividend to get a new dividend: 2x⁵ - x⁴ - (2x⁵ - x⁴) = 0.
4. Bring down the next term, which is - 26x³.
5. Divide - 26x³ by 2x to get - 13x².
6. Multiply the divisor, 2x - 1, by the quotient, - 13x². This gives us - 26x³ + 13x².
7. Subtract this product from the new dividend to get a new dividend: - 26x³ + 13x² - (- 26x³ + 13x²) = 0.
8. Bring down the next term, which is 72x.
9. Divide 72x by 2x to get 36.
10. Multiply the divisor, 2x - 1, by the quotient, 36. This gives us 72x - 36.
11. Subtract this product from the new dividend to get a new dividend: 72x - 36 - (72x - 36) = 0.

Since the new dividend is now 0, there is no remainder. Therefore, the quotient is x⁴ - 13x² + 36 and the remainder is 0.