Question

PTDTTNT:

1. x^2-x-12

2. x^3-y^3-3x^2+3x-1

3. x^2-3xy+2y^2

4. 4X^3-5x^2-16x+20

Answer 1

a)  x² - x - 12 

= x² - 4x + 3x - 12

= x(x - 4) + 3(x - 4)

= (x - 4)(x + 3)

b) x³ - y³ - 3x² + 3x - 1

= (x³ - 3x² + 3x - 1) - y³

= (x - 1)³ - y³

= (x - 1 - y) [ (x - 1)² + (x - 1)y + y² ]

= (x - y - 1)(x² - 2x + 1 + xy - y + y² )

d) 4x³ - 5x² - 16x + 20

= (4x³ - 8x²) + (3x² - 6x) - (10x - 20)

= 4x² (x - 2) + 3x(x - 2) - 10(x - 2)

= (x - 2)(4x² + 3x - 10)

= (x - 2)(4x² + 8x - 5x - 10)

= (x - 2)(x + 2)(4x - 5)