can someone please show me how to get a factor? like

Question

(Factor 9x^3 + 18x^2 – x – 2)

Answer 1

The given expression 9x³+18x²-x-2

Apply synthetic division

x =- 2 |  9    18     -1   -2

            0   -18     0    2

         ________________

           9   0      -1    0

(x + 2) ( 9x²-1)

Factors (x + 2) ( 9x²-1)

 

Answer 2

The function is f(x ) = 9x³ + 18x² - x -2.

If p/q is a rational zero, then p is a factor of 2 and q is a factor of 9.

The possible values of p are   ± 1,   ± 2.

The possible values for q are ± 1,± 3 and   ± 9.

So,real numbers of  p/q = ± 1,   ± 2

Make a table for the synthetic division and test possible real zeros.

p/q	9	18	-1	-2
-1	9	9	-10	8
1	9	27	26	24
-2	9	0	-1	0
2	9	36	73	144

Since f(-2)   =   0,   x  =  -2 is a zero. x + 2 is a root.

The depressed polynomial is  9x² -1

9x² – 1=(3x+1)(3x-1)

Therefore possible factors are (x + 2),(3x+1),(3x-1)