Question

Use factor theorem to factorise the following polynomials completely: 4x³ + 4x² – 9x – 9

Answer 1

 f(x) = 4x³ + 4x² – 9x – 9
Let x = -1, then
f(-1) = 4 (-1)³ + 4 (-1)² – 9 (-1) – 9
= 4(–1) + 4(1) + 9 – 9
= –4 + 4 + 9 – 9
= 13 – 13
= 0
∴ (x + 1) is a factor of f(x)
Now dividing f(x) by x + 1, we get
f(x) = 4x³ + 4x² – 9x – 9
= (x + 1)(4x² – 9)
= (x + 1){(2x)² – (3)²}
= (x + 1)(2x + 3)(2x – 3)

`x + 1")"overline(4x^3 + 4x^2 - 9x - 9)("4x^2 - 9`
            4x³ + 4x²
           –      –                       
                  – 9x –  9
                  – 9x –  9
                  +     +      
                         x