Factored Form Equations

For Quadratic Equations you can calculate the factored form. First I will list the terms for the parts

• Quadratic Term (ax²)
• Linear Term (bx)
• Constant Term(c)

Give the equation

y = x² - 3x -10  

This can be written like this

y = (x -5)(x+2)

The way to approach it is to identify the factors (numbers) when multiplied together add up to the constant (-10) part of the equation and when added together equal the linear (-3x) part of the equation
A more complex quadratic could be

 y = 3x² + 8x + 4

Here we have to multiply the Quadratic Terms number with the constant i.e. 3 x 4 = 12. Then repeat above to find factors which add up to the linear part of the equation but this time we write it linear part split.

 y = 3x² + 6x + 2x + 4

Now we look for common factors

 y = 3x(x + 2) + 2(x + 2)

Now we can use q to equal x + 2

 y = 3xq + 2q

Which factoring out q this can be written as

 y = q(3x + 2)

And we know q = x + 2 so we now have

 y = (x + 2)(3x + 2)

And another example

 y = 2x² - x - 15
 y = 2x² - 6x + 5x  - 15
 y = 2x(x -3) + 5(x -3)
 y = 2xq + 5q
 y = q(2x + 5)
 y = (x - 3)(2x + 5)