Question

I'm having trouble understanding factoring quadratics when a=1

Answer 1

To factor a expression of the form:

`x^2+Bx+C`

we need to find two integers a and b that fulfills the following conditions:

`\begin{gathered} ab=C \\ a+b=B \end{gathered}`

In that way we write the original expression as:

`x^2+Bx+C=x^2+ax+bx+C`

and then we facto by grouping.

Let's make the example to understand this better.

`p^2-12p+20`

In this case B=-12 and C=20. We need to find two numbers that fulfills:

`\begin{gathered} ab=20 \\ a+b=-12 \end{gathered}`

We see that the numbers a=-2 and b=-10, fulfill this conditions. Then we write the expression as:

`p^2-12p+20=p^2-2p-10p+20`

and now we factor the first pair and second pair of terms by common factors:

`\begin{gathered} p^2-12p+20=p^2-2p-10p+20 \\ =p(p-2)-10(p-2) \\ =(p-2)(p-10) \end{gathered}`

Therefore:

`p^2-12p+20=(p-2)(p-10)`