For the polynomial below, 3 is a zero. g(x)=x^3 + x^2 -15x +9 Express g(x) as a product of linear factors.

Question

 For the polynomial below, 3 is a zero. g(x)=x^3 + x^2 -15x +9 Express g(x) as a product of linear factors. 

Answer 1

Use synthetic division.

 

3 | 1       1        -15        9

 

              3         12       -9

_______________________

      1      4         -3         0

 

 

g(x) = (x - 3)(x² + 4x - 3)

 

We can factor out the quadratic if we complete the square.

 

(x² + 4x + 4) - 4 - 3 = (x + 2)² - 7

 

 

Difference in perfect squares.

 

                               = ((x + 2) - √7)((x + 2) + √7)

 

 

g(x) = (x - 3)(x + 2 - √7)(x + 2 + √7)