Download Unit #6 Factoring Polynomials

Factoring
Polynomials
Factoring Polynomials
Binomials
Trinomials
1. GCF
1. GCF
2. Diff of 2 Squares
2. Perfect Square
3. Sum of 2 Cubes
3. Quadratic
4. Diff of 2 Cubes
4. Prime
5. Prime
Greatest Common Factor
1. ALWAYS check for
GCF
2. Find GCF of every
term
3. Divide each term by
GCF
Factor each polynomial
completely
2. 4  x  2y   3m x  2y 
3. 2pr  3r  pw  rwpw  3r 
4. x 2y  3   4 y  3  2y 
2
5.  3x  4  x  2   5x x  2 
Factor each polynomial
2
completely
6. 6
 a  b   a  b
7. 9  2a  7  a  2   15  2a  7 a  2 
2
8. 2  b  3   5 b  3   b  3 
2
9.  2x  1   2x  1
3
10. x x  y   9x
2
5
3
2
Difference of 2 Squares
a² – b² = (a + b)(a – b)
• Both terms are perfect squares
• The operation is subtraction
• The terms in each binomial are the
square root of the terms in the
problem
• One binomial is addition and one
Factor each polynomial
completely
4
1. 1 81x
2. 81x y  144z
20
14
3. 36   2a  1
4. 4x  64
4
32
2
Sum / Difference 2
Cubes
a³ – b³ = (a – b)(a² + ab + b²)
a³ + b³ = (a + b)(a² – ab + b²)
• Both terms are perfect cubes
• Operation may be addition or
subtraction
• The terms are a binomial and a
trinomial
• Rule: Cube root of each term
Factor each polynomial
3
9
completely
1. 8a  125b
2. 27a  64b
6
18
3.  2x  3   27
3
4. 32x y  108x y
5
2 7
Perfect Square
Trinomials
a² + 2ab + b² = (a + b) ²
a² – 2ab + b² = (a – b) ²
• 1st and 3rd terms are perfect
squares
• The middle term is twice the
product of the square roots of the
perfect square terms
Factor each polynomial
2
completely
1. 25x  30x  9
2. 121x  154x y  49 y
16
8
12
3. 4x  24x y  36 xy
3
2
24
2
4. 25  2a  1  30  2a  1  9
2
Quadratic Trinomials
• Guess and Check
Method
• Product Method
• Best Method
Product Method
1. Multiply leading coefficient and constant
2. Determine the factors of this product that
add up to the coefficient of the middle
term
3. Split the middle term and factor by
grouping
4. Find the GCF of each binomial
5. Write the product of your factors
Best Method
1. Multiply leading coefficient and constant
2. Determine the factors of this product that
add up to the coefficient of the middle
term
3. Form 2 binomials using the first term in
each binomial and the 2 factors in
second term in each binomial
4. Divide each binomial by the GCF
5. Write the product of your factors
Factor each polynomial
completely
2
1. x  11x  24
2. x  6 x  16
2
3. 3x  10x  8
2
4. 5x  7x  6
2
Factor each polynomial
completely
2
5. 12x  x  6
6. 8x  2x  15
2
7. 6x  5x  6
2
8. 6x  11x  4
2
4 Term Polynomials
1. Look for a perfect square
trinomial
2. Look for a difference of 2
squares
3. Simplify
Factor by Grouping
1. Grouping can be used with 4
terms
2. Group terms with a common
factor
3. Find the GCF of each binomial
4. Factor out the common term
5. Write polynomial in factored form
Factor each polynomial
2
2
2
1. 4x completely
 25z  y  4xy
3
2
2. x  4x  4x  16
2
2
3. y  x  9  6 x
4
3
4. x  x  8x  8
2
2
5. a  8a  16  9b
6. 24ab  20bd  18ac  15cd
4
2
2
7. 9x  12x  y  4