Question

Find the quotient and remainder. {x⁴-8x²+2x+7}{x+5}

Answer 1

To find the quotient and remainder of the polynomial division {x⁴-8x²+2x+7}/{x+5}, use long division method. The quotient is x³-8x-3 and the remainder is 7.

Step-by-step explanation:

To find the quotient and remainder of the polynomial division {x⁴-8x²+2x+7}/{x+5}, we use long division method:

1. First, divide the first term of the numerator, which is x⁴, by the first term of the denominator, which is x. This gives us x³ as the first term of the quotient.
2. Multiply the entire denominator, x+5, by x³. This gives us x⁴+5x³.
3. Subtract x⁴+5x³ from the numerator {x⁴-8x²+2x+7}.
4. Bring down the next term, which is -8x².
5. Divide -8x² by x. This gives us -8x as the next term of the quotient.
6. Multiply the entire denominator, x+5, by -8x. This gives us -8x²-40x.
7. Subtract -8x²-40x from the remaining part of the numerator.
8. Repeat this process until all terms of the numerator have been divided.
9. The last term of the quotient is 2.
10. The remaining term is 7.

Therefore, the quotient of the polynomial division {x⁴-8x²+2x+7}/{x+5} is x³-8x-3 and the remainder is 7.