Question

How to factor ax2+bx+c

Answer 1

To factor the expression ax² + bx + c, we can use the quadratic formula:

$x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$

where x1, and x2 are the zeros, or roots, of the polynomial. And the factored expression will be:

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

For example, if the expression is 5x² -35x + 60, then a = 5, b = -35 and c = 60. Substituting into the formula we get:

$\begin{gathered} x_{1,2}=\frac{-(-35)\pm\sqrt[]{(-35)^2-4\cdot5\cdot60}}{2\cdot5} \\ x_{1,2}=\frac{35\pm\sqrt[]{25}}{10} \\ x_1=\frac{35+5}{10}=4 \\ x_2=\frac{35-5}{10}=3 \end{gathered}$

Then, the factored expression is:

5x² -35x + 60 = 5(x - 4)(x - 3)