Question

Writef(x) = 6x^3– 5x² – 3x + 2 in factored form given that f(1) = 0

Answer 1

Step 1: Write down the given function

`\begin{gathered} f(x)=6x^3-5x^2-3x+2 \\ f(1)=0 \end{gathered}`

Step 2: Get the factor of f(1)=0

`\begin{gathered} \text{When f(1)=0} \\ (x-1)\text{ is a factor of the function} \end{gathered}`

Step 3: Get the other factors by dividing the function by (x-1)

`(f(x))/(x-1)=(6x^2-5x^2-3x+2)/(x-1)`

Hence,

`(6x^3-5x^2-3x+2)/(x-1)=6x^2+x-2`

To get the other factors, factorize the answer gotten

`\begin{gathered} 6x^2+x-2 \\ 6x^2+4x-3x-2 \\ 2x(3x+2)-1(3x+2) \\ (2x-1)(3x+2) \end{gathered}`

Hence, the factors are (x-1)(2x-1)(3x+2)