Title of notes: GCF and factoring Algebraic Expressions Pg. 27 & 28 RS

Identity Property (multiplication) Bell work Identity Property (multiplication) The number 1 multiplied times any number gives you the number itself

Vocabulary Factors - are numbers you can multiply together to get another number. Each number can have MULTIPLE factors (Time on this slide – 5 min) Time passed 33 min In-Class Notes Read slide as it appears. Conduct a very quick turn and talk about algebraic expressions This worksheet is located on the back of the launch. Be sure to point out that none of the expressions are using an ‘x’ for multiplication. Discuss the similarities and difference of the examples given. Have students read the definitions out loud, and copy onto the worksheet. Go right into the next slide for more vocabulary. Preparation Notes This slide is designed to introduce Algebraic Expressions (the next slide continues with more definitions). Click the slide, reading to the students what 10n is called. Advance the slide again, to have students start thinking why it is called an algebraic expression and not a numerical expression. Conduct a very quick turn and talk. Then take a few answers from students. See what student’s responses are before clicking to show the definition. Advance the slide for examples to appear discussing the similarities and differences of each expression. Also may want to emphasize the variable is any unknown number and what is happening to that particular variable. Again, point out that the ‘x’ is no longer used. Have students read out loud each expression. Now ask students to copy down the definition on the worksheet. (If there is different way vocabulary is designed in your classroom, students do not need to copy down the definitions at this time, but the next slides are highly encouraged to read through with the class.) Click to reveal next part Agenda

Ex: Find the GCF(24, 40). Prime factor each number: 24 2 12 2 6 2 3  24 = 2*2*2*3 = 23*3  GCF(24,40) = 23 = 8 40 2 20 2 10 2 5  40 = 2*2*2*5 = 23*5

The Greatest Common Factor of terms of a polynomial is the largest factor that the original terms share Ex: What is the GCF(7x2, 3x) 7x2 = 7 * x * x 3x = 3 * x The terms share a factor of x  GCF(7x2, 3x) = x

Factoring 7x2 + 3x  7x2 + 3x = x(7x + 3) Think of the Distributive Law: a(b+c) = ab + ac  reverse it ab + ac = a(b + c) Do the terms share a common factor? What is the GCF(7x2, 3x)? Recall: GCF(7x2, 3x) = x Factor out 2  7 x + 3 x = x ( + ) What’s left? x x  7x2 + 3x = x(7x + 3)

Ex: Find the GCF(6a5,3a3,2a2) 6a5 = 2*3*a*a*a*a*a 3a3 = 3*a*a*a The terms share two factors of a  GCF(6a5,3a3,2a2)= a2 Note: The exponent of the variable in the GCF is the smallest exponent of that variable the terms

Ex: Factor 6a5 – 3a3 – 2a2 Recall: GCF(6a5,3a3,2a2)= a2 1 6a5 – 3a3 – 2a2 = a2( - - ) 6a3 3a 2 a2 a2 a2  6a5 – 3a3 – 2a2 = a2(6a3 – 3a – 2)

See if the expanded expression and the algebraic expression are equivalent. Important!!!! Remember what to do about the package a) 6(x + 5) and 6x + 30 b) 4(y – 4) and 4y - 4 c) 7(x + 3) and 21 + 7x Agenda 9