Question

Factor the equationx^2-17x+42

Answer 1

To factor an expression of the form:

`x^2+Bx+C`

we need to find two integers a and b that fullfil:

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

then we write the expression as:

`x^2+ax+bx+C`

and factor by agrupation.

Let's do this with the expression:

`x^2-17x+42`

In this case B=-17 and C=42.

If we take a=-14 and b=-3, then:

`\begin{gathered} (-14)(-3)=42 \\ -14-3=-17 \end{gathered}`

then we write the expression as:

`\begin{gathered} x^2-14x-3x+42=x(x-14)-3(x-14) \\ =(x-3)(x-14) \end{gathered}`

Therefore, the factorize expression is:

`(x-3)(x-14)`