Question

The polynomial (x ^ 2 - 26x - 120) is in the form x ^ 2 + bx + c which can be factored as (x + p)(x + q).Next factor the polynomial x ^ 2 - 26x - 120 . To identify the factors, complete the table: Note: This table does not contain all the factors of-120, but it has enough to let you factor the polynomial.

Answer 1

It is required to factor the given polynomial by completing the table.

The given polynomial is:

`x^2-26x-120`

Add the factors listed in the table to complete the table as follows:

Notice that only the sum of the factors 4 and -30 gives the coefficient of x, -26.

Hence, write -26x as -30x+4x to factorize the polynomial as follows:

`\begin{gathered} x^2-26x-120 \\ =x^2-30x+4x-120 \\ =x(x-30)+4(x-30) \\ =(x+4)(x-30) \end{gathered}`

The answer is (x+4)(x-30).