WHAT IS Factored and expanded form?
Factoring:
There are 2 forms of an quadratic equation. Factored form (FF) and expanded form (EF).
Factored form:
(x+5) (x+6)
Expanded form:
x² + 11x + 30
How to change from factored from (FF) to Expanded Form (EF):
There are 2 forms of an quadratic equation. Factored form (FF) and expanded form (EF).
Factored form:
(x+5) (x+6)
Expanded form:
x² + 11x + 30
How to change from factored from (FF) to Expanded Form (EF):
FF: (x +2) (x+5)
(x + 2) (x +5) x * x = x² x * 2 = 2x x * 5 = 5x 2 * 5 = 10 x² + 5x + 2x +10 ----------> x² + 7x +10 EF: x² + 7x +10 |
STEPS:
1. Multiply both sets of parenthesis together. 2. Simplify the equation by combing like terms 3. Equation is in expanded form. |
How to change from expanded form (EF) to factored form (FF):
EF: x² + 15x +56
a= 1 b= 15 c=56 c-value : 1, 56 2, 28 4, 14 7, 8, 7+8 =15 1+56=57 4+14= 18 7 and 8 2+28= 30 (X +____) (X+____) ( x+7) (x+8) FF: (x+7) (x+8) |
STEPS:
1. Determine the a, b and c- values 2. Make a list of the factors of the c-value 3. Determine which set of factors has a sum that is the same as the b-value. 4. set up the equation or factored form and plug in the integers 5. equation is in factored form |
Examples:
FF ------> EF
(-2x +6) (x-12) -2x*x= -2x² -2x* -12 = 24x 6 * x = 6x 6 * -12 = -72 -2x² + 24x +6x -72 ----------------> -2x² + 30x -72 -2x² + 30x -72 |
EF -------> FF
x² + 2x -35 C-value : -1, 35 -5, 7 -7, 5 35, -1 -1 +35 = 34 -35 +1 = - 34 -5 and 7 -5 + 7 = 2 -7 + 5= -2 (x + __) ( x- __) ---------> (x + 7) (x- 5) (x + 7) (x- 5) |