Quadratic Equation
2x² – 7x –15
I use the FOIL method, terms of the equation are multiplied together and go in the following order.
F)irst
O)uter
I)nner
L)ast
To factor the equation set it up in the format below. The numbers and signs +- need to be tweaked. The terms are multiplied together, the Outer and Inner are multiplied and then added, Last is multiplied. For the First we know x times x equals x² and we need a coefficient of 2, so put in 2x. And we need some numbers that when multiplied equal –15. A little bit of trial and error is needed.
Format
( x + _ ) ( x - _ )
First 2x x
Outer 2x -5
Inner +3 x
Last +3 -5
Factored (2x + 3) (x - 5)
Check the results:
First 2x²
Outer -10x
Inner 3x
Last -15
Showing all the work as not to lose points.
2x² - 10x + 3x -15
Simplified:
2x² -7x – 15
To answer the question of (2x +3) (x – 5), the answers are –1.5, 5.
Dedicated to Mr. Barrett, my algebra teacher.