Question

wo polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x), and express P in the form P(x) = D(x) · Q(x) + R(x). P(x) = 4x² − 3x - 7, D(x) = 2x - 1 P(x) =

Answer 1

To divide the polynomial P(x) = 4x² - 3x - 7 by D(x) = 2x - 1, use long division. The expression P(x) can be written as P(x) = (2x - 1)(2x - 0.5) - 7.5.

Step-by-step explanation:

To divide the polynomial P(x) = 4x² - 3x - 7 by D(x) = 2x - 1 using long division, follow these steps:

1. Start by dividing the leading term of P(x) (4x²) by the leading term of D(x) (2x). The result is 2x.
2. Multiply D(x) by 2x, which gives you 4x² - 2x.
3. Subtract the result from the original P(x): (4x² - 3x - 7) - (4x² - 2x) = -x - 7.
4. Bring down the next term of P(x) (-x).
5. Divide (-x) by 2x, which gives you -0.5.
6. Multiply D(x) by -0.5, which gives you -x + 0.5.
7. Subtract the result from the previous remainder: (-x - 7) - (-x + 0.5) = -7.5.

The remainder is -7.5, so the expression P(x) can be written as P(x) = (2x - 1)(2x - 0.5) - 7.5.