Question

Factor each quadratic expressionx^2-2x-15

Answer 1

When we are factoring a quadratic function, we are trying to reverse the following equation

`(x+a)(x+b)=x^2+(a+b)x+ab`

Now, comparing the right-hand side of the above equation and the one given in the problem we see that

`\begin{gathered} a+b=-2 \\ ab=-15 \end{gathered}`

This means the question simplifies to "what are the two numbers that if I add them I get -2 and if I multiply them I get -15? "

Well, If we set a = -5 and b = 3, then

`\begin{gathered} -5+3=-2 \\ -5\cdot3=-15 \end{gathered}`

Hence, our expression factors to

`(x-5)(x+3)`