In each of the following, divide f x by dx, obtaining quotient qx and remainder rx. Then, write a division statement, i.e. express your answers in the form f x dxqx rx.

Question

x3 3x2 x2x2 3x2 4x4
3x3 7x2 5x13x1 x5 1x1
b) 2x3 4x2 3x5x3
d) 4x3 6x2 6x92x3 f) x4 x3 2x2 3x8x4

Answer 1

a) (x^3 - 3x^2 + x + 2) ÷ (x + 2) = x^2 - 5x + 11

Division statement: (x^3 - 3x^2 + x + 2) = (x + 2)(x^2 - 5x + 11)

b) (3x^2 - 4) ÷ (x - 4) = 3x + 8

Division statement: (3x^2 - 4) = (x - 4)(3x + 8)

c) (3x^3 + 7x^2 + 5x + 1) ÷ (3x + 1) = x^2 + 2x + 1

Division statement: (3x^3 + 7x^2 + 5x + 1) = (3x + 1)(x^2 + 2x + 1)

d) (x^5 - 1) ÷ (x - 1) = x^4 + x^3 + x^2 + x + 1

Division statement: (x^5 - 1) = (x - 1)(x^4 + x^3 + x^2 + x + 1)

e) (2x^3 - 4x^2 - 3x + 5) ÷ (x - 3) = 2x^2 - 10x + 27

Division statement: (2x^3 - 4x^2 - 3x + 5) = (x - 3)(2x^2 - 10x + 27)

f) (4x^3 + 6x^2 - 6x - 9) ÷ (2x + 3) = 2x^2 - 3x - 4

Division statement: (4x^3 + 6x^2 - 6x - 9) = (2x + 3)(2x^2 - 3x - 4)