Question

When dividing the polynomial by long division, identify the numeric remainder.

(x3+2x2−29x+43)÷(x+7)

(a) -56
(b) 56
(c) -43
(d) 43

Answer 1

Upon performing long division of the polynomial (x^3+2x^2-29x+43) by (x+7), we find that the numeric remainder is 43.

Step-by-step explanation:

To find the numeric remainder when dividing the polynomial busing long division, we'll perform the following steps:

1. Divide the leading term of the polynomial by the leading term of the divisor (x3 by x).
2. Multiply the entire divisor by this result and subtract it from the polynomial.
3. Bring down the next term and repeat the process until you reach the constant term.
4. The remainder is the term not divisible by the divisor.

Performing the long division, we get a remainder of 43, which cannot be divided further by (x+7).

Thus, the numeric remainder is 43.