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# Simple factoring

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### Simple factoring

1. 1. Simple Factoring Objective: Find the greatest common factor in and factor polynomials.
2. 2. Greatest common factor (GCF) <ul><li>The largest of the common factors of two or more numbers. </li></ul>
3. 3. Polynomial <ul><li>Many terms containing a combination of variables, constants, and positive exponents that are added. </li></ul>
4. 4. Distributive property <ul><li>Multiplying a single term and a polynomial. </li></ul>
5. 5. Distributive Property Examples and Practice To multiply common bases with exponents: Keep the base and add the exponents. x 2 (x 3 ) = x 5 y 4 (y 7 ) = y 11 z 23 (z 3 ) = z 26 Examples:   2(50 + 3) = 100 + 6 = 106   2(x + 3) = 2x + 6   y(x + 1) = yx + y   y(x + y 2 ) = yx + y 3   Practice:   3(10 + 6)     3(x + 6)   y(x + 6)   y(x + y 4 )
6. 6. Find the Greatest Common Factor Find the greatest common factor: 10 + 5 2x – 4x 3y +6y 2 8d 3 + 4d 2 + 12d
7. 7. Factoring: The distributive property in reverse: <ul><li>Identify the GCF </li></ul><ul><li>Divide each term by the GCF </li></ul><ul><li>Place the GCF in front of parentheses </li></ul><ul><li>Place the remainder in the parentheses </li></ul><ul><li>Check: Does using the distributive property result in the original expression? </li></ul><ul><li>3x + bx </li></ul><ul><li>GCF = x </li></ul><ul><li>3x/x = 3 </li></ul><ul><li>bx/x = b </li></ul><ul><li>3-4) x ( 3 + b ) </li></ul><ul><li>5) 3x + bx </li></ul>
8. 8. Factoring Practice <ul><li>ax – cx </li></ul><ul><li>9x – 3y </li></ul><ul><li>ax – bx </li></ul><ul><li>4x – 12y </li></ul><ul><li>25y – 35y 2 </li></ul><ul><li>12y 2 – 36y 3 + 24y 4 </li></ul>