Question

Find the other binomial p squared -13 p +36 =(p-9)

Answer 1

To find the other factor of the polynomial

`p^2-13p+36`

We need to find two integers which multiplication gives 36 and addition is -13.

This integers would be -9 and -4, then we have

`p^2-13p+36=p^2-9p-4p+36`

now we factor the right term using common factors:

`\begin{gathered} p^2-9p-4p+36=p(p-9)-4(p-9) \\ =(p-9)(p-4) \end{gathered}`

Hence:

`p^2-9p-4p=(p-9)(p-4)`

Therefore, the other binomial we are looking for is (p-4).