Question

Find the remaining zeros of f(x) given that c is a zero. Then rewrite f(x) in completely factored form.f(x) = 3x3 - 8x2 - 5x + 6; c = -1 is a zero

Answer 1

Given:

`f(x)=3x^3-8x^2-5x+6`

c= -1 is the zero of the function.

Use the synthetic division,

Solving it further,

`\begin{gathered} (x-1)(3x^2-11x+6)=0 \\ \text{Solve }3x^2-11x+6=0 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a},a=3,b=-11,c=6 \\ x=(-\left(-11\right)\pm√(\left(-11\right)^2-4\cdot\:3\cdot\:6))/(2\cdot\:3) \\ x=(11\pm7)/(6) \\ x=(11+7)/(6),x=(11-7)/(6) \\ x=3,x=(2)/(3) \end{gathered}`

So, the zeros of the function are,

`\begin{gathered} f(x)=3x^3-8x^2-5x+6 \\ x=-1,3,(2)/(3) \\ f(x)=(x+1)(3x-2)(x-3) \end{gathered}`

Answer: