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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, x 2 – 5x - 9 Polynomials cannot have a variable as a denominator nor negative exponents.

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Are the following polynomials? 7/a ¼ xy – 10 3pq 1/2 √7 x 4 – x 3 8 -2

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Polynomials with one term are called monomials 5x 3, 8, x 2, etc two terms are called binomials 3x – 1, 2x 2 + 8, etc three terms are called trinomials 2x 2 – 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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2x – 1 = degree of 1Constant term of -1 These are called a linear. 2x 2 + 8 = degree of 2 Constant term of 8 These are called quadratic. 2x 3 – 5 = degree of 3 Constant term of -5 These are called cubic.

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EXAMPLE 1 State the degree, coefficient’s and constant term of the polynomial. 5x 3 + x 2 – 7x + 9

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EXAMPLE 2 State the degree, coefficient and constant term of the polynomial. 6a – 4a 2 - 3

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ADDING AND SUBTRACTING POLYNOMIALS Find like terms and combine them in order to simplify polynomials. 4x – 2x 2 + 3 – 6x 2 + 5 – x

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TRY THE FOLLOWING a 2 b – ab 2 + 4a 3 b – 7ab 2 + 5a 2 b (3a – 4b + c) + (3b – 5c – 3a)

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BE CAREFUL WITH SUBTRACTION (4x 2 – 9x + 6) – (2x 2 – 3x – 1)

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Work on Handout

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FACTORING LINEAR POLYNOMIALS 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 4m + 12 GCF = 4 = 4 (m + 3)

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6 – 15a GCF = 3 = 3 (2 – 5a)

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TRY THE FOLLOWING 6n + 9 = 6c + 4c 2 = 3g + 6 = 8d + 12d 2 =

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FACTORING TRINOMIALS ax 2 + bx + c 5 – 10z – 5z 2 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 – z 2 )

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EXAMPLES 18a 2 – 12a + 6 9 + 27x – 45x 2

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FACTORING WITH MORE THAN ONE VARIABLE Find all GCF’s, numbers and letters. -12 x 3 y – 20xy 2 – 16x 2 y 2 GCF for numbers = 4 GCF for letters = 1x and 1y 4xy (-3x 2 – 5y – 4xy)

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5ab 2 + 10a 2 b 3 – 15a 2 b 4

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- 20c 4 d - 30c 3 d 2 – 25cd

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Work on textbook questions # 6, 7, 8, 9, 10, 14.

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