5.3 - 5.4 polynomials

5.3

100

(x-2)(x+7)

x(x) + 7x - 2x - 2(7)

x² + 7x - 2x - 14

= x² + 5x - 14

200

(6x-7)(2x+5)

(6x(2x)) + (6x(5)) - (7(2x)) - 7(5)

12x² + 30x - 14x - 35

= 12x² + 16x - 35

300

(x² + 6x - 5)(4x + 2)

x²(4x+2) + 6x(4x+2) - 5(4x+2)

4x³ + 2x² + 24x² + 12x - 20x - 10 

= 4x³ + 26x² - 8x - 10

5.4

100

(8x³ - 12x) / (4x²)

4x(2x² - 3) / 4x²

= 2x² - 3 / x

200

5x² + 2x + 3 / x+2

= 5x - 8 + 19/x+2

300

(4x² - 2x) / (-x)

4x²/-x - 2x/-x

= -4x + 2