Polynomials

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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

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.

Are the following polynomials?

• 7/a
• ¼ xy – 10
• 3pq1/2
• √7 x4 – x3
• 8-2

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
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.
• 2x2 + 8 = degree of 2 Constant term of 8 These are called quadratic.
• 2x3 – 5 = degree of 3 Constant term of -5 These are called cubic.
Example 1
• State the degree, coefficient’s and constant term of the polynomial.
• 5x3 + x2 – 7x + 9
Example 2
• State the degree, coefficient and constant term of the polynomial.
• 6a – 4a2 - 3
Adding and Subtracting polynomials
• Find like terms and combine them in order to simplify polynomials.
• 4x – 2x2 + 3 – 6x2 + 5 – x
Try the following
• a2b – ab2 + 4a3b – 7ab2 + 5a2b
• (3a – 4b + c) + (3b – 5c – 3a)
Be Careful with subtraction
• (4x2 – 9x + 6) – (2x2 – 3x – 1)
Factoring Linear polynomials
• Just as natural numbers can be factored so can polynomials.
• Find the GCF in each term and then factor.
Factoring Examples
• 4m + 12
• GCF = 4
• = 4 (m + 3)

6 – 15a

• GCF = 3
• = 3 (2 – 5a)
Try the following
• 6n + 9 =
• 6c + 4c2 =
• 3g + 6 =
• 8d + 12d2 =
Factoring Trinomials
• 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)
Examples
• 18a2 – 12a + 6
• 9 + 27x – 45x2
Factoring with more than one variable
• 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)