Examples: How to Factor a Quadratic Equation

Let’s solve the Quadratic Equation $$x^2- 6x+8 = 0$$ .
The 2 zeros when multiplied have to equal 8.
That could be 8 and 1 or 4 and 2, and their negatives.

the 2 zeros must be -4 and -2.

Therefore,
$$x^2- 6x+8 = (x-4)*(x-2)$$ .

Finally, the 2 zeros are $$x=4 , x=2$$
since $$x-4=0$$ yields $$x=4$$ ,
and $$x-2=0$$ yields $$x=2$$ .

Easy, wasn’t it?

Tip: When using the above Quadratic Equation Solver to solve
$$x^2-6x+8=0$$ we must enter the 3 coefficients as
$$a=1, b=-6$$ and $$c=8$$.

Example 2: Factoring Quadratic Equations with leading coefficient a different from 1

We are to solve the Quadratic Equation $$2x^2- 12x+16 = 0$$ .
First divide by 2 to have a leading coefficient coefficient of a=1.
We get $$x^2- 6x+8 = 0$$ just like in the above example.

The 2 zeros when multiplied have to equal 8.
That could be 8 and 1 or 4 and 2, and their negatives.

$$x^2- 6x+8 = (x-4)*(x-2)$$ and also
$$2x^2- 12x+16 = 2*(x-4)*(x-2)$$ .
Finally, the 2 zeros are $$x=4 , x=2$$
since $$x-4=0$$ yields $$x=4$$ ,
and $$x-2=0$$ yields $$x=2$$ .