2.4 part 1 - Basic Factoring
I can...
- Factor using GCF
-Factor a difference of two perfect squares
-Factor basic trinomials
Difference of Two Perfect Squares
When a quadratic is in the form: ax2 – c ; b = 0, c is negative,
and a and c are perfect squares (ex:
1,4,9,16,25,36,49,64,81,100,121…)
To Factor:
1. Square root the first item and place in the first spot of each
parenthesis.
2. Square root the second term and place in the second spot
in each parenthesis.
Example: 4x2 – 9
(2x + 3)(2x – 3)
To Factor and Expression in the Form:
ax2 + bx + c when a=1
Put the equation in standard form FIRST (highest exponent to lowest)
Look to see if you can factor out the GCF (a common factor in ALL terms)
Look to see if you can factor using the difference of two perfect squares.
Look to see what two numbers multiply to get (c) and add to get (b)
These two numbers are placed in the parenthesis
(x +/- ____)(x +/- ____)
FOIL to check
Examples: Factor each expression completely.
1. 5x2 + 30x
The GCF is 5x, so:
5x(x + 6)
2. 15y2 – 10y
The GCF is 5y, so:
5y(3y – 2)
3. 5rs2 + 20r2s
The GCF is 5rs, so:
5rs(s + 4r)
4. x2 – 81
(x + 9)(x – 9)
5. 9x2 – 25
(3x – 5)(3x + 5)
6. 3x2 – 48
The GCF is 3 so we need to factor that out first:
3(x2 – 16)
3(x + 4)(x – 4)
7. 2x2 – 2
The GCF is 2 so we need to factor that out first:
2(x2 – 1)
2(x + 1)(x – 1)
8. -15 + 2x + x2
First write in standard form: x2 + 2x – 15
What multiplies to get -15 AND adds to 2?
5 and -3
So to factor we write our two parenthesis:
(x + 5)(x – 3)
9. 36 – 5x – x2
Standard form: -x2 – 5x + 36
Factor out the (-), so –(x2 + 5x – 36)
Now factor, what multiplies to -36 and adds to 5?
9 and -4
-(x + 9)(x – 4)
10. 30 + 5x – 5x2
Standard form: -5x2 + 5x + 30
Factor out the GCF: -5
-5(x2 – x – 6)
Factor, what multiplies to -6 and adds to -1?
-3 and 2
-5(x – 3)(x + 2)