Question

.Which is a factor of 18x2+ 3x − 6?

2x + 1

2x + 3

3x + 2

3x − 1

Answer 1

\[f(x)=a*(x-x_1)*(x-x_2)\]\[f(x)=18x^2+3x-6\]\[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]\[x=\frac{-3\pm\sqrt{3^2-4*18(-6)}}{2*18}\]\[x=\frac{-3\pm\sqrt{441}}{36}\]\[x_1=\frac{1}{2}~~~~and~~~~x_2=-\frac{2}{3}\]Re-writing the first function\[f(x)=18*\left(x-\frac{1}{2}\right)*\left(x+\frac{2}{3}\right)\]Take both parenthesis \[A)~~x-\frac{1}{2}=2x-1\]\[B)~~x+\frac{2}{3}=\boxed{3x+2}\]
So the correct answer is C:\[\boxed{\boxed{3x+2}}\]