Lesson 2'9 Factor Polynomials Completely

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Lesson 2.9Factor Polynomials Completely

• GPS
• MM1A2f
• EQ
• How do we factor expressions by greatest common
  factor, grouping, trial and error, and special
  products?

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Vocabulary

• Factor by Grouping Factoring a common monomial
  from pairs of terms, then looking for a common
  binomial factor.
• Factored Completely If a factorable polynomial
  with integer coefficients is written as a product
  of unfactorable polynomials with integer
  coefficients.

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Example 1Factor out common binomial

• Factor the expression.
• 5x2(x - 2) - 3(x - 2)
• 7y(5 y) 3(y 5)

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Example 2Factor by grouping

• Factor the polynomial.
• m3 7m2 2m 14
• n3 30 6n2 5n

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Example 3Factor completely

• Factor the polynomial completely.
• 5x3 55x2 90x
• 48y4 3y2

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Guided Practice forExamples 1, 2, and 3

• 11x(x 8) 3(x 8)
• 9x3 9x2 7x 7
• 10x3 21y 35x2 6xy
• 4x3 36x
• 2y3 16y2 32y
• m3 3m2 40m

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Example 4Solve a polynomial equation

• Solve the equation 7x3 14x2 105x.

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Guided Practice for Example 4

• 2c3 8c2 42c 0
• 4x3 48x2 144x 0
• 5r3 15r 20r2

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Joke of the Day

• What vehicle is spelled the same forward and
  backwards?

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• Racecar!