Question

which expression shows the factors of 9x squared plus 3x - 2

Answer 1

$9x^2+3x-2$

we use quadratic formula to find the roots

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

where a is 9, b is 3 and c is -2

replacing

$\begin{gathered} x=\frac{-(3)\pm\sqrt[]{(3)^2-4(9)(-2)}}{2(9)} \\ \\ x=\frac{-3\pm\sqrt[]{9+72}}{18} \\ \\ x=\frac{-3\pm\sqrt[]{81}}{18} \\ \\ x=\frac{-3\pm9}{18} \end{gathered}$

then x has two values

$\begin{gathered} x_1=\frac{-3+9}{18}=\frac{1}{3} \\ \\ x_2=\frac{-3-9}{18}=-\frac{2}{3} \end{gathered}$

Therea area the roots, values when are replaced the solution is 0 then we can write the factors with this numebrs but opposite sign

then

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

to simplify we can multiply each term by 3, to remove the fractions

$(3x-1)(3x+2)$

we can invert the position to compare with third option

$(3x+2)(3x-1)$

then right option is C