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Advanced Algebra
Name _______________________________
P4 Notes: Factoring Polynomials
Objective: In this lesson you learned how to factor polynomials.
Show that f(x) represents a quadratic function.
f ( x)  ( x  2)( x  5)
Can you solve for x?
What was the Zero Product Property?
Now can you solve for x?
What do our answers mean?
Common Factors
Does EACH term have anything (variable or number) in common?
Example 1: 4 x 2  12 x  16
Example 3:
1
x4
2
Example 2: ( x  2)(2 x)  ( x  2)(3)
Example 4:
2
x( x  3)  4( x  3)
3
Difference of Two Squares
Example 5: x 2  16  0
Example 6: 121x 2  196 y 4
Grouping
Example 7: 6 x3  x 2  18 x  3  0
1. Underline the first two terms (together)
and underline the second two terms
2. Work as if they were two separate problems
3. Factor out what's in common in the 1st set
4. Drop the sign
5. Factor out what's in common in the 2nd set
6. Parenthesis should match
7. Factor out the common parenthesis
Example 8: 144 x5  18 x 4  120 x3  15 x 2  0
Trinomials
Example 9: x 2  7 x  10  0
1. Multiply a and c together.
2. Bring down the 1st & last term.
3. What 2 numbers multiply to be
"a x c" and add/sub to be "b"
4. Split the middle term
5. Grouping
6. Take out what's in common
7. Solve for x.
Example 10: 6 x 2  11x  3  0
Example 11: 15 x 2  4 x  4  0
Example 12: 8 x 2  6 x  35  0
Example 13: 8 x 2  18 x  9  0
Perfect Square Trinomials
Example 14: 4 x 2  24 x  36  0
1. Take the square root of the first and last term.
2. Check to see if those two new terms multiplied together
and then doubled equal the middle term.
3. Place the two new terms in a parenthesis.
4. Put the first sign from the trinomial in the parenthesis.
5. Square the parenthesis. (put a little 2 outside the
parenthesis on the right)
Example 15: 16 x 2  16 x  1  0
Steps of Factoring
Mixed Practice
1. 18 y3  32 y
2. 250a 3  2b3
3. 6h3  23h 2  13h
4. 35 y 3  10 y 2  25 y
5. x 2  4 x3  4 x  x 4
6. (t  1)2  49
7. 5(3  4 x)2  8(3  4 x)(5 x  1)
8. 3( x  2)2 ( x  1)4  ( x  2)3 (4)( x  1)3