Question

`x { }^(2) - 11x - 26`factor the polynomial.

Answer 1

`\begin{gathered} \text{Factor the polynomial;} \\ x^2-11x-26 \\ \text{The factors of the constant -26 are 2 and -13} \\ (x+2)(x-13) \end{gathered}`

The factors are derived as (x + 2) and (x - 13)

When factoring polynomials of a second degree (that is the highest variable is raised to the power of two like in quadratic equations), then you take the constant and break it down into two factors (for example, -26 can be broken down into -13 x 2, or 13 x -2). Next you identify which of the factors would sum up to the coefficient of the variable with the power of 1. In this case which of the factors would add up to -11. The factors are -13 and +2 which gives -11

Therefore the factors would be x - 13 and x + 2