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# Polynomials - PowerPoint PPT Presentation

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

• 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.

• 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

• 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

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

• Constant term: term without a variable.

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

• 5x3 + x2 – 7x + 9

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

• 6a – 4a2 - 3

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

• 4x – 2x2 + 3 – 6x2 + 5 – x

• a2b – ab2 + 4a3b – 7ab2 + 5a2b

• (3a – 4b + c) + (3b – 5c – 3a)

• (4x2 – 9x + 6) – (2x2 – 3x – 1)

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

• Find the GCF in each term and then factor.

• 4m + 12

• GCF = 4

• = 4 (m + 3)

• 6n + 9 =

• 6c + 4c2 =

• 3g + 6 =

• 8d + 12d2 =

• 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)

• 18a2 – 12a + 6

• 9 + 27x – 45x2

• 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)

• 5ab a 2 + 10a2b3 – 15a2b4

• - a 20c4d - 30c3d2 – 25cd