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Mastering Polynomial Factoring: GCF and Monomial Factors

Dive into the essential concept of polynomial factoring with our comprehensive guide. Learn how to identify the Greatest Common Factor (GCF) in various polynomial terms, and apply this understanding to factor expressions effectively. Practice problems involve finding the GCF in polynomials like 3x² + 6x - 18, as well as factoring monomials and binomials. Get hands-on experience with exercises such as factoring 6x - 4 and 8x² - 12x. This valuable skill will serve you throughout your algebra journey. Submit your completed worksheet by the end of the period!

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Mastering Polynomial Factoring: GCF and Monomial Factors

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  1. Warm Up • Fill in the missing factor. • (3a2)( ) = 6a3 • (-2x)( ) = 8x5y • (x2y3)( ) = 5x2y • Find the GCF of the terms of the polynomial. A. 3x2 + 6x – 18 B. 4x3 – 6x2 + 12x

  2. 9.2 Part III Monomial Factors Today is the start of an important concept in algebra – factoring. We will be factoring for the rest of the year. Factoring is like doing the distributive property in reverse or “undoing” the distributive property

  3. Factoring out the Greatest Monomial Factor of a Polynomial • Identify the GCF of the terms of the polynomial. It is possible that the GCF is 1. • Write the GCF of the terms on the outside of a left parenthesis GCF( • Write what you would need to multiply the GCF by to get the terms of the original polynomial. • Check your work by using the distributive property.

  4. Ex1 Factor 6x – 4. • What is the GCF of the terms? 6x = 2 · 3 · x 4 = 2 · 2 The GCF = 2 • Write the GCF on the outside of a parenthesis: 2( • Write what you need to multiply 2 by to get back to the original polynomial. 2(3x – 2) Check: 2(3x – 2) = 6x - 4 Write 2, since 2(2) = 4 Write 3, since 2(3) = 6 Use – since the terms of the original polynomial are separated by a -

  5. Ex2 Factor v2 + 4v Ex3 Factor 3x3 + 9x2

  6. Ex4 Factor 5d3 + 10d Ex5 Factor 10y3 + 5y2 – 15y

  7. Your turn. Factor. • 8x2 – 12x • 6m2 – 12m – 24

  8. Assignment: worksheet 81 You must write the problems on your warm up paper and show your work. The worksheet is due at the end of the period.

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