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5.3.1 - Factoring

5.3.1 - Factoring. With quadratics, we can both expand a binomial product like (x + 2)(x + 5), or similar, and go the other way around Factoring = taking a quadratic (trinomial) and writing it in terms of its binomial products. Methods for factoring:

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5.3.1 - Factoring

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  1. 5.3.1 - Factoring

  2. With quadratics, we can both expand a binomial product like (x + 2)(x + 5), or similar, and go the other way around • Factoring = taking a quadratic (trinomial) and writing it in terms of its binomial products

  3. Methods for factoring: • GCF = greatest common factor; find the biggest factor the numbers have in common • Tree = using a tree to come up of the factors of a particular number, then writing as the product

  4. GCF • When using the GCF, most common for when only factoring a binomial • Consider the greatest factor for both the variable and the coefficients

  5. Example. Factoring the expression 4x2 + 8x • Smallest power of variable? • Largest number coefficients have in common?

  6. Example. Factoring the expression 5y3 – 15y2 • Smallest power of variable? • Largest number coefficients have in common?

  7. Factor the following three expressions using the GCF. • 1) 10x3 + 5x • 2) 3x2 – 9x3 • 3) 15y4 – 3y

  8. “Tree” • With trinomials, or quadratics with three terms, we can factor them into their respective binomial factors • The trick will be to use factor trees, similar to those used in classes before

  9. Using trees • To use the three, consider the expression x2 + 4x + 3 • We need the factors of the constant that will add to the middle • Factors of 3?

  10. Example. Factor the expression x2 + 6x + 8 • Factors of constant? • Which add to the middle?

  11. Example. Factor the expression x2 - 3x - 10 • Factors of constant? • Which add to the middle?

  12. Example. Factor the expression x2 + 2x - 15 • Factors of constant? • Which add to the middle?

  13. Assignment • PG. 237 • 15-31 odd

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