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Polynomials. Lesson 3.3 Factoring. Polynomials. A math equation consisting of one to many terms. Examples: 6, x , 6x, -1/2xy , 2y + x, x 2 – 5x - 9 Polynomials cannot have a variable as a denominator nor negative exponents. Are the following polynomials? 7/a ¼ xy – 10

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Polynomials

Lesson 3.3 Factoring


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Polynomials

  • A math equation consisting of one to many terms.

  • Examples:

  • 6, x, 6x, -1/2xy, 2y + x, x2 – 5x - 9

  • Polynomials cannot have a variable as a denominator nor negative exponents.


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  • Polynomials with

  • one term are called monomials

  • 5x3, 8, x2, etc

  • two terms are called binomials

  • 3x – 1, 2x2 + 8, etc

  • three terms are called trinomials

  • 2x2 – 4x + 9


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  • Variables – a letter that represents one or more numbers

  • 4y = y is the variable

  • Coefficient – number in front of a variable

  • 4y = coefficient is 4


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Degrees of a polynomial

  • The degree of a polynomial is the degree of the term with the highest exponent.

  • Constant term: term without a variable.


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Example 1 a

  • State the degree, coefficient’s and constant term of the polynomial.

  • 5x3 + x2 – 7x + 9


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Example 2 a

  • State the degree, coefficient and constant term of the polynomial.

  • 6a – 4a2 - 3


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Adding and Subtracting polynomials a

  • Find like terms and combine them in order to simplify polynomials.

  • 4x – 2x2 + 3 – 6x2 + 5 – x


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Try the following a

  • a2b – ab2 + 4a3b – 7ab2 + 5a2b

  • (3a – 4b + c) + (3b – 5c – 3a)


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Be Careful with subtraction a

  • (4x2 – 9x + 6) – (2x2 – 3x – 1)



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Factoring Linear polynomials a

  • Just as natural numbers can be factored so can polynomials.

  • Find the GCF in each term and then factor.


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Factoring Examples a

  • 4m + 12

  • GCF = 4

  • = 4 (m + 3)


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Try the following a

  • 6n + 9 =

  • 6c + 4c2 =

  • 3g + 6 =

  • 8d + 12d2 =


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Factoring Trinomials a

  • ax2 + bx + c

  • 5 – 10z – 5z2

  • Find the GCF of all three terms.

  • In this example the GCF is 5.

  • Factor out a 5 from each and write as a product.

  • 5 ( 1 – 2z – z2)


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Examples a

  • 18a2 – 12a + 6

  • 9 + 27x – 45x2


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Factoring with more than one variable a

  • Find all GCF’s, numbers and letters.

  • -12 x3y – 20xy2 – 16x2y2

  • GCF for numbers = 4

  • GCF for letters = 1x and 1y

  • 4xy (-3x2 – 5y – 4xy)


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  • 5ab a 2 + 10a2b3 – 15a2b4


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  • - a 20c4d - 30c3d2 – 25cd