Question

Factor the quadratic expression1.x^2 + 5x - 142.x^2 + 7x + 6

Answer 1

A quadratic equation can be rewritten as

`ax^2+bx+c=a(x-x_1)(x-x_2)`

where x1 and x2 represents the roots of the quadratic equation.

To find those roots we can use the quadratic equation. Given a quadratic equation with the following form

`ax^2+bx+c=0`

its roots are given by

`x_(\pm)=(-b\pm√(b^2-4ac))/(2a)`

In our first quadratic equation, we have

`x^2+5x-14`

therefore, its roots are

`\begin{gathered} x_(\pm)=(-(5)\pm√((5)^2-4(1)(-14)))/(2(1)) \\ =(-5\pm√(25+56))/(2) \\ =(-5\pm9)/(2) \\ \implies\begin{cases}x_-={-7} \\ x_+={2}\end{cases} \end{gathered}`

Then, this quadratic expression can be factorized as

`x^2+5x-14=(x+7)(x-2)`

Using the same process for the other expression, we have

`x^2+7x+6=(x+1)(x+6)`