Answer to Question #158697 in Physics for moon

Question

Divide P(x) by D(x) using synthetic division. Write P(x) in the form Q(x)D(x) + R(x).

1. P(x) = x⁴ + x³ - 3x² - 5x - 2; D(x) = x - 2
2. P(x) = x³ - 9x - 12; D(x) = x + 3
3. P(x) = -2x³ - 5x⁴ + 2x⁵ - 3x + 1; D(x) = 2x - 1
4. P(x) = 4x⁴ - 3x² + x - 17; D(x) = 2x + 3

Answer 1

1)

$$\frac{ ( x^4 + x^3 - 3x^2 - 5x - 2)}{( x - 2)}=x^3 + 3x^2 +3x +1$$

2)

$$\frac{ ( x^3 - 9x - 12)}{( x+3)}=x^2 -3x -\frac{12}{( x+3)}$$

3)

$$\frac{ ( -2x^3 - 5x^4 + 2x^5 - 3x + 1)}{( 2x-1)}=x^4 -2x^3-2x^2 -x-2\\-\frac{ 1}{( 2x-1)}$$

4)

$$\frac{ ( 4x^4 -3x^2+x-17)}{( 2x+3)}=2x^3-3x^2+3x-4\\-\frac{ 5}{( 2x+3)}$$