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Factors and Factoring Polynomials: GCF and Factor Box

Learn how to find the greatest common factor (GCF) of a polynomial using a Factor "T" method and complete factor boxes to factor polynomials. Practice factoring 4-term polynomials.

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Factors and Factoring Polynomials: GCF and Factor Box

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  1. Warm Up • Multiply using the area model or distribution: • 3x2( x + 5) • 2. Use the Area Model to multiply the following: • (2x + 4) (x - 2)

  2. Math I UNIT QUESTION: In what ways can algebraic methods be used in problems solving? Standard: MM1A2 Today’s Question: How do we find the GCF of a polynomial? Standard: MM1A2f

  3. 3 EASY PIECESFactor “T” & Factor “X” & Factor Box This is a guide for FACTORING POLYNOMIALS X-Box

  4. What is Factoring?

  5. What is Factoring? To understand factoring we’ll first break down what multiplying is: MULTIPLYING: (MONOMIAL)• ( MONOMIAL) = PRODUCT OR (FACTOR)• ( FACTOR) = PRODUCT

  6. What is the first thing you should check when factoring polynomials?

  7. What is the first thing you should check when factoring polynomials? Are there any common factors (numbers or variables) with All of the terms? In other words does a GCF exist? GCF?

  8. What is the GCF?

  9. Use a Factor “T” A factor “T” is a method of Finding the GCF

  10. Use a Factor “T” GCF Find the greatest common # & variable

  11. Use a Factor “T” GCF Divide the GCF into each term to complete factoring

  12. Do A Mental Check GCF Mental Check

  13. Mental Check Mental Check Use this to indicate you have Completed a mental check.

  14. We can represent this problem as a Factor Tree Product • Factor Factor

  15. Factor GCF Factor “T”

  16. Factor GCF Factor “T” 1. Find Greatest Common Number • 2. Find Greatest Common Variable GCF

  17. Factor GCF Factor “T” 1. Find Greatest Common Number • 2. Find Greatest Common Variable • 3. Divide GCF into each Term GCF

  18. Factor GCF Factor “T” 1. Find Greatest Common Number • 2. Find Greatest Common Variable • 3. Divide GCF into each Term • 4. Do a Mental Check Mental Check 10x2(x-2)

  19. Factor GCF Factor “T”

  20. Factor GCF Factor “T” 1. Find Greatest Common Number • 2. Find Greatest Common Variable GCF

  21. Factor GCF Factor “T” 1. Find Greatest Common Number • 2. Find Greatest Common Variable • 3. Divide GCF into each Term GCF

  22. Factor GCF Factor “T” 1. Find Greatest Common Number • 2. Find Greatest Common Variable • 3. Divide GCF into each Term • 4. Do a Mental Check GCF Mental Check

  23. Factor GCF Factor “T”

  24. Factor GCF Factor “T” 1. Find Greatest Common Number • 2. Find Greatest Common Variable GCF

  25. Factor GCF Factor “T” 1. Find Greatest Common Number • 2. Find Greatest Common Variable • 3. Divide GCF into each Term GCF

  26. Factor GCF Factor “T” 1. Find Greatest Common Number • 2. Find Greatest Common Variable • 3. Divide GCF into each Term • 4. Do a Mental Check GCF Mental Check

  27. Factor GCF Factor “T”

  28. Factor GCF Factor “T” 1. Find Greatest Common Number • 2. Find Greatest Common Variable GCF

  29. Factor GCF Factor “T” 1. Find Greatest Common Number • 2. Find Greatest Common Variable • 3. Divide GCF into each Term GCF

  30. Factor GCF Factor “T” 1. Find Greatest Common Number • 2. Find Greatest Common Variable • 3. Divide GCF into each Term • 4. Do a Mental Check GCF Mental Check

  31. Factor GCF Factor “T”

  32. Factor GCF Factor “T” 1. Find Greatest Common Number • 2. Find Greatest Common Variable GCF

  33. Factor GCF Factor “T” 1. Find Greatest Common Number • 2. Find Greatest Common Variable • 3. Divide GCF into each Term GCF

  34. Factor GCF Factor “T” 1. Find Greatest Common Number • 2. Find Greatest Common Variable • 3. Divide GCF into each Term • 4. Do a Mental Check GCF Mental Check

  35. GCF Factoring Practice

  36. GCF Factoring Practice

  37. Factoring 4 Term Polynomialswith Factor Box

  38. x3+3x2+2x+6 Factoring 4 Term Polynomials

  39. x3+3x2+2x+6 Factoring 4 Term Polynomials Put 4 terms in boxes in descending order. 1 2 x3 3x2 3 4 2x 6

  40. x3+3x2+2x+6 Factoring 4 Term Polynomials Put 4 terms in boxes in descending order. 2. Use a Factor “T” to find GCF of upper boxes. 1 2 x3 3x2 x2 3 4 2x 6

  41. x3+3x2+2x+6 Factoring 4 Term Polynomials x +3 Put 4 terms in boxes in descending order. 2. Use a Factor “T” to find GCF of upper boxes. 3. Complete Top Factor 1 2 x3 3x2 x2 3 4 2x 6

  42. x3+3x2+2x+6 Factoring 4 Term Polynomials x +3 Put 4 terms in boxes in descending order. 2. Use a Factor “T” to find GCF of upper boxes. 3. Complete Top Factor 4. Complete Side Factor. 1 2 x3 3x2 x2 3 4 +2 2x 6

  43. x3+3x2+2x+6 Factoring 4 Term Polynomials x +3 Put 4 terms in boxes in descending order. 2. Use a Factor “T” to find GCF of upper boxes. 3. Complete Top Factor 4. Complete Side Factor. 5. Answer is Top Factor times Side Factor 1 2 x3 3x2 x2 3 4 +2 2x 6 =(x+3)(x2+2)

  44. x3+x2+4x+4 Factoring 4 Term Polynomials

  45. x3+x2+4x+4 Factoring 4 Term Polynomials Put 4 terms in boxes in descending order. 1 2 x3 x2 3 4 4x 4

  46. x3+x2+4x+4 Factoring 4 Term Polynomials Put 4 terms in boxes in descending order. 2. Use a Factor “T” to find GCF of upper boxes. 1 2 x3 x2 x2 3 4 4x 4

  47. x3+x2+4x+4 Factoring 4 Term Polynomials x +1 Put 4 terms in boxes in descending order. 2. Use a Factor “T” to find GCF of upper boxes. 3. Complete Top Factor 1 2 x3 x2 x2 3 4 4x 4

  48. x3+x2+4x+4 Factoring 4 Term Polynomials x +1 Put 4 terms in boxes in descending order. 2. Use a Factor “T” to find GCF of upper boxes. 3. Complete Top Factor 4. Complete Side Factor. 1 2 x3 x2 x2 3 4 +4 4x 4

  49. x3+x2+4x+4 Factoring 4 Term Polynomials x +1 Put 4 terms in boxes in descending order. 2. Use a Factor “T” to find GCF of upper boxes. 3. Complete Top Factor 4. Complete Side Factor. 5. Answer is Top Factor times Side Factor 1 2 x3 x2 x2 3 4 +4 4x 4 =(x+1)(x2+4)

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