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

Which of the following is a factor of the polynomial Step By Step Explanation Please-example-1

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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.

User Ryanwinchester
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