21
g Polynomi als

Factoring Polynomials. 1.Check for GCF 2.Find the GCF of all terms 3.Divide each term by GCF 4.The GCF out front 5.Remainder in parentheses Greatest Common

Embed Size (px)

Citation preview

Factoring Polynomi

als

1.Check for GCF2.Find the GCF of all

terms3.Divide each term by

GCF4.The GCF out front5.Remainder in

parentheses

Greatest Common Factor

Factor each polynomial completely.

Factor each polynomial completely.

Factor each polynomial completely.

• 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 binomial is subtraction

Difference of 2 Squares

a² – b² = (a + b)(a – b)

Factor each polynomial completely.41. 1 81x

20 14 322. 81x y 144z

23. 36 2a 1

44. 4x 64

Sum / Difference 2 Cubesa³ – 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• Rule: Square / Opposite Product /

Square

Factor each polynomial completely.3 91. 8a 125b

6 182. 27a 64b

33. 2x 3 27

5 2 74. 32x y 108x y

• 1st and 3rd terms are perfect squares

• The middle term is twice the product of the square roots of the perfect square terms

Perfect Square Trinomials

a² + 2ab + b² = (a + b) ²

a² – 2ab + b² = (a – b) ²

• The terms in the binomial are the square roots of the perfect square terms in the problem

• The operation is the same as the middle term

Perfect Square Trinomials

Factor each polynomial completely.

3 2 23. 4x 24x y 36xy

24. 25 2a 1 30 2a 1 9

Quadratic Trinomials• Guess and Check

Method• Product Method• Best Method

1. Multiply the leading coefficient and the constant term

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 binomial5. Write the product of your factors

Product Method

1. Multiply the leading coefficient and the constant term

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 GCF5. Write the product of your factors

Best Method

Factor each polynomial completely.

21. x 11x 24 22. x 6x 16 23. 3x 10x 8 24. 5x 7x 6

Factor each polynomial completely.

25. 12x x 6 26. 8x 2x 15 27. 6x 5x 6 28. 6x 11x 4

4 Term Polynomials1. Look for a perfect square

trinomial2. Group and factor the perfect

square trinomial3. Look for a difference of two

squares4. Factor the difference of two

squares5. Simplify

Factor each polynomial completely.

4 2 24. 9x 12x y 4

2 23. a 8a 16 9b

2 22. y x 9 6x

2 2 21. 4x 25z y 4xy

1. Grouping can be used with 4 terms

2. Group terms with a common factor

3. Find the GCF of each binomial4. Factor out the common term5. Write polynomial in factored

form

Factor by Grouping

Factor each polynomial completely.3 21. x 4x 2x 8

3 22. x 2x x 2

4 33. x x x 1