Question

a) x³ -4x² - 8x + 8

b) 1 + 6x - 6x² - x² 

^c) 6x³ -x² - 486x + 81

d) x⁴ - 4x² +4x - 1

e) x² ( x² + 4 ) - x² + 4

Answer 1

a) \(x^3-4x^2-8x+8\)

\(=x^3+8-4x^2-8x\)

\(=\left(x+2\right)\left(x^2-2x+4\right)-4x\left(x+2\right)\)

\(=\left(x+2\right)\left(x^2-2x+4-4x\right)\)

\(=\left(x+2\right)\left(x^2-6x+4\right)\)

\(=\left(x+2\right)\left(x^2-6x+9-5\right)\)

\(=\left(x+2\right)\left[\left(x-3\right)^2-5\right]\)

\(=\left(x+2\right)\left(x-3-\sqrt{5}\right)\left(x-3+\sqrt{5}\right)\)

Answer 2

b) \(1+6x-6x^2-x\)

\(=1-x+6x\left(1-x\right)\)

\(=\left(1-x\right)\left(6x+1\right)\)

Answer 3

c) \(6x^3-x^2-486x+81\)

\(=x^2\left(6x-1\right)-8x\left(6x-1\right)\)

\(=\left(6x-1\right)\left(x^2-8x\right)\)

\(=x\left(6x-1\right)\left(x-8\right)\)

Answer 4

\(x^4-4x^2+4x-1\)

\(=x^4-1-4x^2+4x\)

\(=\left(x-1\right)\left(.........\right)-4x\left(x-1\right)\)

\(=\left(x-1\right)\left(......-4x\right)\)