Question

How do I factor f(x)=3x^3+2x^2-19x+6 as a product of linear factors using synthetic division?

Answer 1

`\begin{gathered} f(x)=3x^3+2x^2-19x+6 \\ a)\text{ f(2)=}3(2)^3+2(2)^2-19(2)+6 \\ \text{f(2)=}3(8)^{}+2(4)^{}-19(2)+6 \\ \text{f(2)=}24^{}+8-38+6 \\ \text{f(2)=38}-38 \\ f(2)=0 \\ x=2\text{ is a zero of f(x)} \\ \\ b)\text{ Factoring f(x)} \\ 3x^3+2x^2-19x+6=(x-2)(3x-1)(x+3) \end{gathered}`