bell quiz. objectives learn to simplify expressions using the greatest common factor or gcf
TRANSCRIPT
![Page 1: Bell Quiz. Objectives Learn to simplify expressions using the greatest common factor or GCF](https://reader035.vdocument.in/reader035/viewer/2022062421/56649ccf5503460f9499b35c/html5/thumbnails/1.jpg)
Bell Quiz
![Page 2: Bell Quiz. Objectives Learn to simplify expressions using the greatest common factor or GCF](https://reader035.vdocument.in/reader035/viewer/2022062421/56649ccf5503460f9499b35c/html5/thumbnails/2.jpg)
Objectives
• Learn to simplify expressions using the greatest common factor or GCF.
![Page 3: Bell Quiz. Objectives Learn to simplify expressions using the greatest common factor or GCF](https://reader035.vdocument.in/reader035/viewer/2022062421/56649ccf5503460f9499b35c/html5/thumbnails/3.jpg)
Prime Factorization
• Simplifying expression that contain numbers often requires knowledge of prime number and factors.
• Recall that a prime number is a whole number that is only divisible by itself and 1.
• All whole numbers other than 1 that are not prime are composite numbers.
• Composite numbers have whole-number factors other than 1 and the number itself.
• They can be written as a product of prime numbers, which is called prime factorization.
![Page 4: Bell Quiz. Objectives Learn to simplify expressions using the greatest common factor or GCF](https://reader035.vdocument.in/reader035/viewer/2022062421/56649ccf5503460f9499b35c/html5/thumbnails/4.jpg)
Prime Factorization
• Several methods can be used to find the prime factorization of a number.
• The process requires breaking down the composite umbers until all the factors are prime.
• The Prime factorization for number 24 can be found in at least three ways.
![Page 5: Bell Quiz. Objectives Learn to simplify expressions using the greatest common factor or GCF](https://reader035.vdocument.in/reader035/viewer/2022062421/56649ccf5503460f9499b35c/html5/thumbnails/5.jpg)
Prime FactorizationExample
The Prime factorization for number 24 can be found in at least three ways.
• It does not matter which method is used to find a prime factorization.
![Page 6: Bell Quiz. Objectives Learn to simplify expressions using the greatest common factor or GCF](https://reader035.vdocument.in/reader035/viewer/2022062421/56649ccf5503460f9499b35c/html5/thumbnails/6.jpg)
Example 1Finding the Prime Factorization of a Number
Find the prime factorization of the number.
120
![Page 7: Bell Quiz. Objectives Learn to simplify expressions using the greatest common factor or GCF](https://reader035.vdocument.in/reader035/viewer/2022062421/56649ccf5503460f9499b35c/html5/thumbnails/7.jpg)
Example 2Finding the Prime Factorization of a Number
Find the prime factorization of the number.
924
![Page 8: Bell Quiz. Objectives Learn to simplify expressions using the greatest common factor or GCF](https://reader035.vdocument.in/reader035/viewer/2022062421/56649ccf5503460f9499b35c/html5/thumbnails/8.jpg)
Lesson Practice
Find the prime factorization of the number.
100
![Page 9: Bell Quiz. Objectives Learn to simplify expressions using the greatest common factor or GCF](https://reader035.vdocument.in/reader035/viewer/2022062421/56649ccf5503460f9499b35c/html5/thumbnails/9.jpg)
Lesson Practice
Find the prime factorization of the number.
51
![Page 10: Bell Quiz. Objectives Learn to simplify expressions using the greatest common factor or GCF](https://reader035.vdocument.in/reader035/viewer/2022062421/56649ccf5503460f9499b35c/html5/thumbnails/10.jpg)
Greatest Common Factor
• Prime factorization can be used when determining the Greatest Common Factor (GFC) of Monomial.
• The GFC of a monomial is the product of the greatest integer that divides without remainder into the coefficients and the greatest power of each variable that divides without a remainder into each term.
• Finding the GCF means finding the larges monomial that divides without a remainder into each term of a polynomial.
![Page 11: Bell Quiz. Objectives Learn to simplify expressions using the greatest common factor or GCF](https://reader035.vdocument.in/reader035/viewer/2022062421/56649ccf5503460f9499b35c/html5/thumbnails/11.jpg)
Example 3Determining the GCF of Algebraic Expession
Find the GCF of the expression.
6a2b3 + 8a2b2c
![Page 12: Bell Quiz. Objectives Learn to simplify expressions using the greatest common factor or GCF](https://reader035.vdocument.in/reader035/viewer/2022062421/56649ccf5503460f9499b35c/html5/thumbnails/12.jpg)
Example 4Determining the GCF of Algebraic Expression
Find the GCF of the expression.
24m3n4 + 32mn5p
![Page 13: Bell Quiz. Objectives Learn to simplify expressions using the greatest common factor or GCF](https://reader035.vdocument.in/reader035/viewer/2022062421/56649ccf5503460f9499b35c/html5/thumbnails/13.jpg)
Lesson Practice
Find the GCF of the expression.
8c4d2e – 12c3d4e2
![Page 14: Bell Quiz. Objectives Learn to simplify expressions using the greatest common factor or GCF](https://reader035.vdocument.in/reader035/viewer/2022062421/56649ccf5503460f9499b35c/html5/thumbnails/14.jpg)
Lesson Practice
Find the GCF of the expression.
5p2q5r2 – 10 pq2r2
![Page 15: Bell Quiz. Objectives Learn to simplify expressions using the greatest common factor or GCF](https://reader035.vdocument.in/reader035/viewer/2022062421/56649ccf5503460f9499b35c/html5/thumbnails/15.jpg)
Factoring Polynomials
• Finding the GCF of a polynomial allows you to factor it and to write the polynomial as a product of factors instead of the sum or difference of monomials.
• Factoring a polynomial is the inverse of the Distributive Property.
• Using the Distributive Property will “undo” the factoring of the GCF.
![Page 16: Bell Quiz. Objectives Learn to simplify expressions using the greatest common factor or GCF](https://reader035.vdocument.in/reader035/viewer/2022062421/56649ccf5503460f9499b35c/html5/thumbnails/16.jpg)
Example 5Factoring a Polynomial
Factor the polynomial completely.
6x3 + 8x2 – 2x
![Page 17: Bell Quiz. Objectives Learn to simplify expressions using the greatest common factor or GCF](https://reader035.vdocument.in/reader035/viewer/2022062421/56649ccf5503460f9499b35c/html5/thumbnails/17.jpg)
Lesson Practice
Factor the polynomial completely.
8d2e3 + 12d3e2
![Page 18: Bell Quiz. Objectives Learn to simplify expressions using the greatest common factor or GCF](https://reader035.vdocument.in/reader035/viewer/2022062421/56649ccf5503460f9499b35c/html5/thumbnails/18.jpg)
Example 6Factoring a Polynomial
Factor the polynomial completely.
9x4y2 – 9x6y
![Page 19: Bell Quiz. Objectives Learn to simplify expressions using the greatest common factor or GCF](https://reader035.vdocument.in/reader035/viewer/2022062421/56649ccf5503460f9499b35c/html5/thumbnails/19.jpg)
Lesson Practice
Factor the polynomial completely.
12x4y2z – 42x3y3z2
![Page 20: Bell Quiz. Objectives Learn to simplify expressions using the greatest common factor or GCF](https://reader035.vdocument.in/reader035/viewer/2022062421/56649ccf5503460f9499b35c/html5/thumbnails/20.jpg)
Algebraic Fractions
• Fractions can be simplified if the numerator and denominator contain common factors.
• This is because the operations of multiplication and division undo each other.
• An algebraic fraction can only be simplified if the numerator and the denominator have common factors.
![Page 21: Bell Quiz. Objectives Learn to simplify expressions using the greatest common factor or GCF](https://reader035.vdocument.in/reader035/viewer/2022062421/56649ccf5503460f9499b35c/html5/thumbnails/21.jpg)
Example 7Simplifying Algebraic Fractions
Simplify the expression
3p + 3 3
![Page 22: Bell Quiz. Objectives Learn to simplify expressions using the greatest common factor or GCF](https://reader035.vdocument.in/reader035/viewer/2022062421/56649ccf5503460f9499b35c/html5/thumbnails/22.jpg)
Lesson Practice
Simplify the expression
6x + 18 6
![Page 23: Bell Quiz. Objectives Learn to simplify expressions using the greatest common factor or GCF](https://reader035.vdocument.in/reader035/viewer/2022062421/56649ccf5503460f9499b35c/html5/thumbnails/23.jpg)
Example 8Simplifying Algebraic Fractions
Simplify the expression
5x – 25x2 5xy
![Page 24: Bell Quiz. Objectives Learn to simplify expressions using the greatest common factor or GCF](https://reader035.vdocument.in/reader035/viewer/2022062421/56649ccf5503460f9499b35c/html5/thumbnails/24.jpg)
Lesson Practice
Simplify the expression
18x + 45x3 9x
![Page 25: Bell Quiz. Objectives Learn to simplify expressions using the greatest common factor or GCF](https://reader035.vdocument.in/reader035/viewer/2022062421/56649ccf5503460f9499b35c/html5/thumbnails/25.jpg)
Example 9Application: Finding the Height of an Object
The formula h = –16t2 + 72t + 12 can be used to represent the height of an object that is launched into the air from 12 feet off the ground with an initial velocity of 72 feet/second. Rewrite the formula by factoring the right side using the GCF and making the t2–term positive.
![Page 26: Bell Quiz. Objectives Learn to simplify expressions using the greatest common factor or GCF](https://reader035.vdocument.in/reader035/viewer/2022062421/56649ccf5503460f9499b35c/html5/thumbnails/26.jpg)
Lesson Practice
The formula h = –16t2 + 60t + 4 can be used to find the height of an object that is launched into the air from 4 feet off the ground with an initial velocity of 60 feet/second. Rewrite the formula by factoring the right side using the GCF and making the t2–term positive.