Question

(2x² + 15x+20) ÷ (x+5)

Answer 1

Answer:

To divide polynomials, we need to use polynomial long division. First, we divide the first term of the dividend by the first term of the divisor to get the first term of the quotient, which we write above the division bar. In this case, the first term of the dividend is 2x² and the first term of the divisor is x, so the first term of the quotient is 2x. We then multiply the divisor by the quotient and subtract it from the dividend to get the remainder.

Here's how the long division would look:

2x² + 15x + 20
===
x + 5

2x

_______

 15x - 10x

 15x + 20 - 10x - 20

 ___________

    5x - 20

After we perform the polynomial long division, we get the quotient 2x + 5 and the remainder -20. Therefore, the final result of the division is:

(2x² + 15x + 20) ÷ (x + 5) = 2x + 5 + (-20)/(x + 5)

Note that the remainder -20 is written as a fraction with the divisor x + 5 in the denominator. This is the correct way to write the remainder because it tells us that the remainder has a degree that is one less than the degree of the divisor. In this case, the degree of the divisor is 1, so the degree of the remainder is 0.