Factoring Quadratics Worksheet With Answers
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1
2Factoring Quadratics
The approaches used in factoring expressions depend on the number of terms that the expression contains.
Remember that your factoring can always be checked by multiplying it out.
2 Terms
3 Terms
1. Factor out GCF*
1. Factor out GCF*
2. Difference of
2. Trinomial with a
Squares:
leading coefficient of 1:
2
2
2
a
- b
x
+ bx + c
3. Trinomial with a
leading coefficient other
than 1:
2
ax
+ bx + c
*No matter how many terms an expression has, factoring out the GCF should always be done FIRST .
Factoring a Difference of Squares:
Both terms must be perfect squares, and they must be separated by subtraction. If so,
2
2
factors into ( a – b ) ( a + b )
a
- b
2
– 16 = ( x – 4) (x + 4)
Examples:
x
2
– 25 = ( 3x – 5 ) ( 3x + 5 )
9x
Factoring Quadratic Trinomials with Leading Coefficient of 1:
2
x
+ bx + c factors into ( x + p) (x + q) by finding the values of p and q that meet the following criteria:
Finding p and q:
1. List all possible pairs of factors of c. Remember to include + / - .
2. Determine which factors will add together to give the middle coefficient, b.
Note:
If no factors can be found, it does not factor with this method.
2
Example: x
- 12x + 27
Step 1) Factors of c.
1, 27
-1, -27
3, 9
-3, -9
Step 2) Sum of factors equals middle coefficient, b.
1 + 27 = 28
-1 + (- 27) = -28
3 + 9 = 12
-3 + (- 9) = -12
Now, you can write the factored form (x + p) ( x + q) by placing the correct factors p and q.
(x - 3)(x - 9)
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