Lesson 5.2.1

How to factor trinomial of the form x²+ bx + c

 Example: x²- 12x- 28

* First, you look at the problem like this ax² +bx+ cà ax² - 12x - 28

* You multiply a by c à the answer is 28

* Now, you must find a number that if multiplied together equals -28 and added together equals b which is -12à the numbers are -14 and 2

* Next, you reconstruct the equation by taking out b (12x) and instead putting in -14 and 2à x² + 2x – 14x-28            

NOTE: you should put the two new numbers where they would be most easily be factored

The factoring now begins

• You next group the numbers together (x² + 2x) (-14x – 28)
• Look at the first parenthesis firstà (x² + 2x)à take out what is common
•  x ( x + 2)
• Now look at the second set of parenthesis (-14x + 28)à take out what is common
• -14 ( x+ 2)
• Put the equations togetherà x (x+2) -14 (x +2) NOTE: the both equations inside the parenthesis must be the same
• The final equation would be (x+2) (x-14)ß THERES YOUR ANSWER!

The Difference of Two Squares

a²- b²= (a+b)(a-b)

 Example: (x + 3) ( x -3)

*This is mental math; you must think what square of 3 isà its 9

*  So the answer is (x² -9) 

Perfect Square Trinomial

9y²+24+16

*There are two options to solve this, you can you the first way mentioned orà (3y)² + 2 (3y) (4) + 4²

*The answer would be (3y + 4)² because the square root of 9 is 3 and the square root of 16 is 4

Standard Form

Standard Formà ax² + bx + c =0

Example : x² +3x-18= 0

*You should first ignore the zero

* You would solve the equation the same way shown earlier ( look at the first part)

* If done right you would have ended up with this equation à (x+6)(x-3)

* Now that you have your two equations, take ( x+6) out

* (x+6)= 0 à x = -6

*Now take out (x-3)

* (x – 3)= 0 à x = 3

* Your two answersà x= -6 & x = 3

Practice Problems

5x² + 5x -10

x² – 3x- 4= 0

x² + 19x + 88 = 0