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Polynomials

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

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  1. Polynomials Lesson 3.3 Factoring

  2. 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.

  3. Are the following polynomials? • 7/a • ¼ xy – 10 • 3pq1/2 • √7 x4 – x3 • 8-2

  4. 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

  5. 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

  6. 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.

  7. 2x – 1 = degree of 1 Constant term of -1 These are called a linear. • 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.

  8. Example 1 • State the degree, coefficient’s and constant term of the polynomial. • 5x3 + x2 – 7x + 9

  9. Example 2 • State the degree, coefficient and constant term of the polynomial. • 6a – 4a2 - 3

  10. Adding and Subtracting polynomials • Find like terms and combine them in order to simplify polynomials. • 4x – 2x2 + 3 – 6x2 + 5 – x

  11. Try the following • a2b – ab2 + 4a3b – 7ab2 + 5a2b • (3a – 4b + c) + (3b – 5c – 3a)

  12. Be Careful with subtraction • (4x2 – 9x + 6) – (2x2 – 3x – 1)

  13. Work on Handout

  14. Factoring Linear polynomials • Just as natural numbers can be factored so can polynomials. • Find the GCF in each term and then factor.

  15. Factoring Examples • 4m + 12 • GCF = 4 • = 4 (m + 3)

  16. 6 – 15a • GCF = 3 • = 3 (2 – 5a)

  17. Try the following • 6n + 9 = • 6c + 4c2 = • 3g + 6 = • 8d + 12d2 =

  18. 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)

  19. Examples • 18a2 – 12a + 6 • 9 + 27x – 45x2

  20. 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)

  21. 5ab2 + 10a2b3 – 15a2b4

  22. -20c4d - 30c3d2 – 25cd

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

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