1 / 17

Factoring Polynomials - PowerPoint PPT Presentation

Factoring Polynomials. Chapter 8.1 Objective 1. Recall: Prime Factorization. Finding the G reatest C ommon F actor of numbers. The GCF is the largest number that will divide into the elements equally. Find the GCF of 3 and 15. 1 st find the prime factors of 3 and 15

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

PowerPoint Slideshow about 'Factoring Polynomials' - dagan

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Factoring Polynomials

Chapter 8.1 Objective 1

• Finding the Greatest Common Factor of numbers.

• The GCF is the largest number that will divide into the elements equally.

• Find the GCF of 3 and 15.

• 1st find the prime factors of 3 and 15

• 3=13 15=13 5

• Determine the GCF by taking common factor (as it occurs the least & occurs in all elements) .

• 1and 3 occurs in both 3 and 15 so,

• GCF = 1 3 = 3 (1 can be the GCF of some elements).

Find the GCF of Variables.

• The GCF is the common variable that will divide into the monomials equally.

• Find the GCF of x3 and x5.

• 1st find the prime factors of x3 and x5

• x3=x x x x5=x x x x x

• Determine the GCF by largest common factor (as it occurs the least & occurs in all monomials) .

• x x x occurs in both x3 and x5 so,

• GCF = x x x = x3

Find the GCF of 12a4b and 18a2b2c

• Find Prime Factors each monomial

• 12a4b = 2 2 3a a a ab

• 18a2b2c = 23 3 a ab bc

• To find GCF consider common factors (must occur in all monomials).

• GCF = 2 3a2b = 6a2b* c is not in GCF because it does not occur in each monomial*

Find the GCF of 4x6y and 18x2y6

• Factor each monomial

• 4x6y = 2 2 x x x x x x y

• 18x2y6 = 2 3 3 x xy y y y y y

• To find GCF consider common factors (must occur in all monomials).

• GCF = 2x2y = 2x2y

• Recall Distributive Property.

• 5x(x+1) = 5x2 + 5x

• The objective of factoring out GCF is to extract common factors.

• Factor 5x2 + 5x by finding GCF.

• What is the GCF of 5x2 + 5x?

• 5x is the GCF, but when you factor 5x out, you must divide the polynomial by the GCF. 5x (5x2 + 5x)

• 5x 5x = 5x(x+1)

Factor 14a2 – 21a4b

• Find GCF of each monomial.

• 14a2 = 2 7a a

• 21a4b = 3 7a a aab GCF = 7a2

• Factor out GCF

• 7a2 (14a2 – 21a4b)

• Divide by GCF7a2 7a2

• 7a2 (2 - 3a2 b)

Factor. 6x4y2 – 9x3y2 +12x2y4

• Find GCF of each monomial

• 6x4y2 = 2 3 x x x xyy

• 9x3y2 = 3 3 x x xy y

• 12x2y4 = 2 2 3x xyy y y

• Factor 3x2y2(6x4y2 – 9x3y2 +12x2y4)

• Divide by GCF3x2y2 3x2y2 3x2y2

• 3x2y2 (2x2 – 3x + 4y2)

• Factor the following.

• 1. 10y2 – 15y3z

• 5y2(2 – 3yz)

• 2. 12m2 +6m -18

• 6(2m2 + m- 3)

• 3. 20x4y3 – 30x3y4 +40x2y5

• 10x2y3 (2x2 - 3xy + 4y2)

• 4. 13x5y4 – 9x3y2 +12x2y4

• x2y2 (13x3y2 - 9x + 12y2)

Chapter 8.1Objective 2

Factor by grouping

When a polynomial has four unlike terms, then consider factor by grouping.

• For the next few examples, the binomials in parenthesis are called binomial factors

• Factor binomial factors as you would monomials.

• Factor y(x+2)+3(x+2)

• (x+2)[y(x+2)+3(x+2)]

• Divide by GCF (x+2) (x+2)

• (x+2)[y+3]

• = (x+2)(y+3)

Factor a(b-7)+b(b-7) factor by grouping.

• Factor binomial factor as you would monomials.

• (b-7)[a(b-7) +b(b-7)]

• Divide by GCF (b-7) (b-7)

• (b-7)[a+b]

• = (b-7)(a+b)

Factor a(a-b)+5(b-a) factor by grouping.

• Notice the binomials are the same except for the signs. You can factor out a -1 from either binomial to make binomials the same

• a(a-b)+5(-1)(-b+a)

• Binomials are the same

• Factor GCF (a-b)[a(a-b)-5(-b+a)]

• Divide by GCF (a-b) (-b+a)

• (a-b)[a-5]

• (a-b) (a-5)

Factor 3x(5x-2) - 4(2-5x) factor by grouping.

• Factor out a -1 from either factor.

• 3x(-1)(-5x+2)-4(2-5x)

• -3x(-5x+2)-4(2-5x)

• Factor GCF (2-5x)[-3x(-5x+2)-4(2-5x)]

• Divide byGCF(-5x+2) (2-5x)

• (2-5x) [-3x-4]

• (2-5x) (-3x- 4)

Factor 3y factor by grouping.3-4y2-6y+8

• Try grouping into binomials to find a binomial factor (sometimes monomials must be rearranged to get binomial factors).

• GCFy2(3y3- 4y2) GCF-2(-6y+8)

• y2(3y- 4) -2(3y-4)

• Factor (3y-4)[y2(3y-4)-2(3y-4)]

• Divide byGCF(3y-4) (3y-4)

• (3y-4) [y2 -2]

• (3y-4) (y2 -2)

Factor y factor by grouping.5-5y3+4y2-20 by grouping.

• Find GCFy3(y5-5y3) +4(4y2-20)

• Divide by GCF y3 y3 4 4

• y3 (y2-5) +4 (y2-5)

• Factor Binomial Factor

• (y2-5)[ y3 (y2-5) +4 (y2-5)]

• Divide by GCF(y2-5) (y2-5)

• (y2-5)[y3+4 ]

• (y2-5)(y3+4 )

Now You Try! factor by grouping.

• 1. 6x (4x+3) -5 (4x+3)

• (4x+3)(6x-5)

• 2. 8x2- 12x - 6xy + 9y

• (2x-3)(4x-3y)

• 3. 7xy2- 3y + 14xy - 6

• (7xy-3)(y+2)

• 4. 5xy - 9y – 18 + 10x

• (5x-9)(y+2)