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1.3-2: Factoring Polynomials

1.3-2: Factoring Polynomials. Factoring = reversing multiplication/decomposing a polynomial Factors will prove useful later on Write as a product of two (or more) polynomials If we can’t, known as irreducible. Greatest Common Factor.

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1.3-2: Factoring Polynomials

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  1. 1.3-2: Factoring Polynomials

  2. Factoring = reversing multiplication/decomposing a polynomial • Factors will prove useful later on • Write as a product of two (or more) polynomials • If we can’t, known as irreducible

  3. Greatest Common Factor • One method to identify a Greatest Common Factor (GCF) among all the terms • Includes the coefficients and exponents • Largest number coefficients have in common • Look for least exponent (power) • Example. Factor, using the GCF:

  4. Example. Factor:

  5. Grouping • Sometimes, not all of the terms share a GCF • But, maybe certain terms share a GCF • Grouping = combine terms so a GCF may be identified • Looking for a like polynomial • Trial, error

  6. Example. Factor:

  7. Factoring Trinomials • With a trinomial, a pattern can be discerned • For polynomials of the form , looking for factors of the constant c which add to the coefficient b

  8. Example. Factor: • What factors of -15 can you think of? • Example. Factor:

  9. Factoring with different a values • For the case of , when , have to look at guessing and checking. • Factors of a; factors of c • Example. Factor:

  10. Example. Factor:

  11. Fractional Exponents • Generally, fractional exponents are not seen • To factor fractional exponents, we first look for the least exponent among the terms • Also factor out any GCFs, if necessary • Usually, will have an additional polynomial to factor as well (intermediate step)

  12. Example. Factor: • What is the least exponent? Careful when working with your exponents/fractions

  13. Assignment • Pg. 52 • #29-55 • Due Thursday (2+ days!)

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