Factor the polynomial completely:

{eq}a^2 - 11a - 42 {/eq}

Question:

Factoring by Grouping

In mathematics, to factor a trinomial of the form {eq}Ax^2 + Bx + C {/eq} by grouping, these steps below will explain how it works.

• First, identify the values of {eq}A,B \text{ and } C {/eq}

• Then, find the product of the leading coefficient "{eq}A {/eq}" and the constant "{eq}C {/eq}"

• Next, look for the factors of the product of "{eq}AC {/eq}" that is equal to the coefficient of {eq}x-term {/eq}, "{eq}B {/eq}"

• Rewrite the middle term "{eq}Bx {/eq}" as a sum or difference of the factors "{eq}AC {/eq}" that add to "{eq}B {/eq}"

• Group the first and second terms into one and the same goes for the third and fourth terms
• Finally, factor out the common term for each group

Answer and Explanation: 1