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Factoring Expressions Warm-Up Lesson: Finding GCF, Writing Equivalent Expressions

Learn to find the greatest common factor (GCF) of numerical sets, factor expressions, and write equivalent expressions. Understand coefficients and terms of expressions. Practice factoring numerical and algebraic expressions.

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Factoring Expressions Warm-Up Lesson: Finding GCF, Writing Equivalent Expressions

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  1. WarmUp Problem of the Day Lesson Presentation Lesson Quizzes

  2. Do Now Find the GCF of each set of numbers. 1. 12 and 50 3. 30 and 45 2. 18 and 30 4. 16, 24 and 30 5. 72, 80 and 96 2 15 6 2 8

  3. SWBAT factor numerical and algebraic expressions and write equivalent numerical and algebraic expression.

  4. Vocabulary term coefficient equivalent expressions

  5. The terms of an expression are the parts that are added or subtracted. The terms of the expressions 140+4x are 140 and 4x. In the term 4x, the 4 is called the coefficient. A coefficient is the number that is multiplied by a variable.

  6. Equivalent expressions are expressions that have the same value as one another but are written differently. The expressions 15x+18 and 3(5x+6) are equivalent expressions. 15x+18=3(5x+6) because of the Distributive Property. You can use the greatest common factor (GCF) and the Distributive Property to factor numerical expressions.

  7. Ex. 1 Factor the sum of terms as a product of the GCF and a sum. 27+39 The terms are 27 and 39 3( ) The GCF of the terms is 3, so place 3 on the outside of the parenthesis 27 + 39 Now write the remaining factors inside of the parenthesis 3 913 3 3(9+13)

  8. Goals for factoring expressions • Identify the terms 2. Find the GCF • Place it outside of the parenthesis 3. Determine the remaining factors • Place them inside of the parenthesis

  9. Ex. 2 Factor the sum of terms as a product of the GCF and a sum. Goals for factoring expressions 15+45 1. Identify the terms 2. Find the GCF • Place it outside of the parenthesis 3. Determine the remaining factors • Place them inside of the parenthesis 15( ) 15 + 45 15 1 3 15 15(1+3)

  10. Ex. 3 Factor the sum of terms as a product of the GCF and a sum. Goals for factoring expressions 12b + 28 1. Identify the terms 2. Find the GCF • Place it outside of the parenthesis 3. Determine the remaining factors • Place them inside of the parenthesis 4( ) 12b + 28 4 3b 7 4 4(3b+7)

  11. Ex. 4 Factor the sum of terms as a product of the GCF and a sum. 16b+32 16(b+2)

  12. Helpful Hint There are many other ways to write equivalent expressions for each of the expressions in Example 3.

  13. Ex. 5 Write 3 equivalent expressions for each given expression. A. 9+15 9+15 3( ) 3(3+5) 3(8) 24

  14. The 3 expressions • 1st expression • Factored Form • 2nd expression • Combine the terms inside of the parenthesis • 3rd expression • Multiply

  15. Ex. 6 B. 25m-5m 25m-5m The terms are 25m and 1m 1st Form 5m() 5m(5 – 1) 5m(4) 2nd Form 20m 3rd Form

  16. Ex. 7 C. 2(4p+2)

  17. Ex. 8 Write three equivalent expressions for each given expression. 3(9p+3)

  18. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  19. Lesson Quiz Factor the sum of terms as a product of the GCF and a sum 15(3+1) 1. 45 + 15 8(3+5) 2. 24 + 40 4(4y+9) 3. 16y + 36 30(3+2s) 4. 90 + 60s

  20. Continued: Lesson Quiz Write all equivalent expressions for each given expression. 5. 20 - 8 4(5-2); 4.3; 12 6. 9z + 12 3(3z+4)

  21. Lesson Quizzes Lesson Quiz for Student Response Systems 1. Factor the sum of terms as a product of the GCF and a sum 60+30

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