Question

Factor the quadratic expression WITH FORMULA 5x^2 - 11x + 2

Answer 1

Given the Quadratic Expression:

$5x{}^2-11x+2$

You can identify that it has this form:

$ax^2+bx+c$

Then, you can use the Quadratic Formula to find its x-intercepts:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

In this case:

$\begin{gathered} a=5 \\ b=-11 \\ c=2 \end{gathered}$

Therefore, by substituting values into the formula and evaluating, you get:

$x=\frac{-(-11)\pm\sqrt{(-11)^2-4(5)(2)}}{2(5)}$$x_1=\frac{11+\sqrt{81}}{10}=2$$x_2=\frac{11-\sqrt{81}}{10}=\frac{1}{5}$

Knowing the x-intercepts, you can write the expression in Factored Form:

$=(x-2)(5x-1)$

Hence, the answer is:

$=(x-2)(5x-1)$