Question

Factor each expression completely6x^2+x-2

Answer 1

`6x^2+x-2`

first , set the function equal to zero

`6x^2+x-2=0`

now we can use this expression to factor

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

where a is 6, b is 1 and c -2

so, replacing

`\begin{gathered} \frac{-(1)\pm\sqrt[]{1^2-4(6)(-2)}}{2(6)} \\ \\ \frac{-1\pm\sqrt[]{1+48}}{12} \\ \\ \frac{-1\pm\sqrt[]{49}}{12} \\ \\ x=(-1\pm7)/(12) \end{gathered}`

x has two values

`x_1=(-1+7)/(12)=(1)/(2)`
`x_2=(-1-7)/(12)=-(2)/(3)`

we have the two roots now we chang the sign and make the factor expression

`(x-(1)/(2))(x+(2)/(3))`