Quadratics
Factoring to turn to Factored Form
Complex Trinomials
Complex trinomials are trinomials with a value of a that it greater than 1, or in other words, there is a coefficient in front of the x^2.
To factor a complex trinomial, if a greatest common factor can be taken out, then take out the greatest common factor. If a greatest common factor cannot be taken out, then use the same chart used to factor simply tinomials. However, this time, the term x^2 will have an a-value, so the factors of ax^2 will not just be x and x, since we need to find factors for the coefficient as well.
EXAMPLE
y = 3x^2 - 12 + 36
To factor this expression, first take out the greatest common, but since there are none, go ahead and put this equation into the chart:
- 12x
3x^2 36
x
3x
Note how this time, the factors of 3x^2 are 1x and 3x, since when they are multiplied, the answer will be 3x^2.
Next, we still need to find 2 numbers that will multiply to 36 and add to -12. However, since there is a coefficient in front of the 'x' on the left side of the chart, we must cross multiply it to the right side.
- 12x
3x^2 36
x
3x
Due to this step, the chart will look like this, since the coefficients in front of the 'x' are being multiplied to the values on the right side of the table:
- 12x
3x^2 36
x
3x
3( )
1( )
The hard part is over because now we need to fond 2 numbers that multiply to 36 and add to -12.
2 numbers that will multiply to 36 and add to -12 are -2 and -6. This is because when -2 is put into the parantheses after 3 in the right column, 3 gets multiplied by -2 to give a product of -6.
Whereas for the next number, -6, when it gets multiplied by 1, it gives a product of -6.
- 12x
3x^2 36
-6 x -6 = 36
-6 + -6 =-12
Therefore, the factored for the equation y = 3x^2 - 12x + 36 is:
(x - 2) (3x - 6)
x
3x
3(-2) = -6
1(-6 ) = -6