Question

Use the long division method to find the

result when 2x³ + 13x² − 4x − 14 is
divided by 2x + 1. If there is a remainder,
express the result in the form q(x) +
r(x)
b(x)*

Answer 1

Explanation:

The long division method is a method of finding the result of dividing a polynomial by a linear polynomial.

To use the long division method, we divide the polynomial by the linear term in the divisor (in this case, 2x + 1). We then multiply the divisor by the result and subtract it from the polynomial, and repeat the process until we are left with a remainder.

For 2x³ + 13x² − 4x − 14 divided by 2x + 1, the process is as follows:

2x³ | 2x + 1

2x² + 2x

-------------

13x² + 4x

-------------

13x² + 12x + 14

-------------

14

-------------

So the result is 2x² + 2x + 7, with a remainder of 14.

Therefore, the answer is q(x) = 2x² + 2x + 7 and r(x) = 14, in the form q(x) + r(x).