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

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

x has two values

$x_1=\frac{-1+7}{12}=\frac{1}{2}$$x_2=\frac{-1-7}{12}=-\frac{2}{3}$

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

$(x-\frac{1}{2})(x+\frac{2}{3})$