Using synthetic division,
the factors of the given polynomial :
[tex]4x^3+5x^2-18x+9[/tex]
Assume x = 1
If the resulting number at the lower left is 0, the assumed value of x is factor.
Now we have a factor of x = 1 or (x - 1) = 0
Next, we have the remaining equation :
[tex]4x^2+9x-9[/tex]
Assume x = -3
The resulting number at the lower is also 0, so x = -3 is a factor or (x + 3) = 0
The remaining equation will be :
[tex]4x-3[/tex]
Therefore, we have the three factors :
The answer is
[tex](x-1)(x+3)(4x-3)[/tex]
