Unit 2: Expressions and Polynomials

1 / 10

Unit 2: Expressions and Polynomials - PowerPoint PPT Presentation

Unit 2: Expressions and Polynomials. GCF and Factoring. GCF. Greatest Common Factor The largest factor in common between two numbers Ex: The GCF between 25 and 30 is 5 Ex: The GCF between 4x and 10 is 2 Ex: The GCF between 5mnp and 15mp is 5mp. GCF and Factoring.

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

PowerPoint Slideshow about 'Unit 2: Expressions and Polynomials' - rodney

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

Unit 2: Expressions and Polynomials

GCF and Factoring

GCF
• Greatest Common Factor
• The largest factor in common between two numbers
• Ex: The GCF between 25 and 30 is 5
• Ex: The GCF between 4x and 10 is 2
• Ex: The GCF between 5mnp and 15mp is 5mp
GCF and Factoring
• Factor the GCF out of the following polynomial
Factoring Polynomials Bottoms Up!
• To factor polynomials in the form
• Use the Bottoms Up Method
• This method works for factoring any type of polynomial!
Bottoms Up! Steps
• Step 1: Multiply a and c together
• Step 2: Find 2 number that multiply to give (ac) and add to give b
• Step 3: Place each of those numbers inside of separate binomials with x at the beginning
• Step 4: Divide each of the constants by a
• Step 5: If any constant is in fraction form, multiply each term in that binomial by the denominator
Factoring Polynomials: Bottoms Up!
• Example:
• Factor
• Step 1: Multiply a and c together
• 1 x 45 = 45
• Step 2: Two numbers that multiply to give 45 and add to give 14
• 9 and 5
• Step 3: Place each number inside of binomials
• (x + 9) (x + 5)
• Step 4: Divide each of the constants by a
• a equals 1, so there is no need to divide further.
Factoring Polynomials: Bottoms Up!
• Factor the following polynomial:
• Step 1: Multiply a and c together
• 2 x 18 = 36
• Step 2: Two numbers that multiply to give 36 and add to give 15
• 12 and 3
• Step 3: Place each number inside of binomials
• (x + 12) (x + 3)
Factoring Polynomials: Bottoms Up!
• Step 4: Divide each of the constants by
• Step 5: Since is not an integer, multiply the 2nd binomial by 2 to get rid of the fraction.