Question

Using polynomial long division, solve: (x^3+4x^2-31x-70)/(x2+2x-35) Show work.

Answer 1

The polynomial long division of (x^3+4x^2-31x-70)/(x^2+2x-35) yields a quotient of x + 6 and a remainder of -1, resulting in the answer x + 6 - 1/(x^2 + 2x -35). The process involves dividing the leading terms and subtracting the exponents of exponential terms, then repeating this until the remainder is of a lower degree than the denominator.

Step-by-step explanation:

To solve the polynomial long division of (x^3+4x^2-31x-70)/(x^2+2x-35), we need to divide the polynomial in the numerator by the polynomial in the denominator. Let's go through the steps:

1. Divide the leading term of the numerator, which is x^3, by the leading term of the denominator, which is x^2. We get x because when we divide the exponential terms, we subtract the exponents. So, x^3 divided by x^2 is x^(3-2) = x.
2. Multiply the entire denominator by x and subtract this from the numerator.
3. Repeat the process with the new polynomial (the result of the subtraction).
4. Continue this process until the degree of the remainder is less than the degree of the denominator.
5. Once done, express the result as the quotient plus the remainder over the original denominator.

After completing these steps, we find that the quotient is x + 6 and the remainder is -1. Thus, the result of the division is x + 6 - 1/(x^2 + 2x -35).

Remember to eliminate terms wherever possible to simplify the algebra and check the answer to see if it is reasonable.

Answer 2

It is difficult to right all steps, but I will give you the answer:

(x^3+4x^2-31x-70)/(x2+2x-35) = (x²+2x-35)(x+2) & the remainder is zero