Question

Which of the following is a factor of the polynomial Step By Step Explanation Please

Answer 1

Use the quadratic formula.

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

Where a = 3, b = -31, and c = -60.

`x=\frac{-(-31)\pm\sqrt[]{(-31)^2-4(3)(-60)}}{2(3)}`

Solve to find both solutions.

`x=\frac{31\pm\sqrt[]{961+720}}{6}=\frac{31\pm\sqrt[]{1681}}{6}=(31\pm41)/(6)`

Rewrite the expression as two.

`\begin{gathered} x_1=(31+41)/(6)=(72)/(6)=12 \\ x_2=(31-41)/(6)=(-10)/(6)=-(5)/(3) \end{gathered}`

Once we have the solutions, we express them as factors. To do that, we have to move the constant to the right side of each equation.

`\begin{gathered} x=12\to(x-12) \\ x=-(5)/(3)\to(3x+5)_{} \end{gathered}`

As can observe, the factor of the polynomial is (x-12).

Therefore, the answer is d.