POLYNOMIALS-REVIEW.ppt
- 1. POLYNOMIALS REVIEW Classifying Polynomials Adding & Subtracting Polynomials Multiplying Polynomials
- 2. Remember: Monomials are separated by _____ or _____ signs.
- 3. But, what is a monomial? A number or variable or product of numbers and variables. 5x2 6 x - y2 z3 ½xy
- 4. “Poly” means _________________? Polynomials can be classified according to the number of terms they have. • ONE TERM – • TWO TERMS – • THREE TERMS -
- 5. 5 5 3 6 2 x x y z z Classify the following: 3x2 – 8xy 4abc 3x2 – 8xy 5x2 a2 + 2ab + b2
- 6. DEGREE……………… The degree of a monomial is determined by adding the exponents of its variables. So, to find the degree of a POLYnomial, find the degree of each separate MONOmial. The Monomial with the HIGHEST sum determines the degree of the problem.
- 7. 5 5 3 6 2 x x y z z 2 3 5 x 7 6 4 4 3 y y x m
- 8. Ascending & Descending Order • Ascending – means to count up! So, order the VARIABLES exponents from least to greatest. • Descending – means to count down! So, order the VARIABLES exponents from greatest to least.
- 9. 2 3 5 4 2 x x x 3 2 4 5 2 x x x 2 3 2 4 24 12 6 x y x y x 3 2 12x y 2 24x y 4 6x 2 3 5 4 2 x x x 3 4x 2 x 2 5x 2 3 2 4 24 12 6 x y x y x 2 3 2 4 24 12 6 x y x y x ( of “y” )
- 10. 2 2 5 8 x y 20 3 3 8 2 x y 6
- 11. Adding & Subtracting Polynomials 2 (3 5 6) y y 2 (7 9) y 2 10y 5y 15 2 2 (3 3 ) a ab b 2 (4 6 ) ab b 2 3a 7ab 2 5b 2 (3 2) x (9x 1) 2 (7x 4 ) x 2 10 5 1 x x
- 12. 2 2 (4 3 5 ) x y xy (8xy 2 6x 2 3 ) y 2 2 2 3 6 x xy y Subtract 2 8 5 x x from 2 2 6 x x 2 3x 2x 5 4 (8 6) x 2 (4x 2) 4 (2x 2 ) x 4 2 10 5 8 x x
- 13. Multiplying Polynomials 3 4 (3 3 ) x x y 4 12 12 x xy 4 5 (8 5 ) x x y 5 40x 25 4 x y 4 3 2 3 (2 4 4 6) x x x x 6 7 x 12 6 x 12 5 x 18 4 x
- 14. 2 2 3 6 ( 4 2 ) x y x xy y 4 6x y 3 2 24x y 2 4 12x y 2 2 3 2 ( 4 7 ) x y x xy y 4 2x y 3 2 8x y 2 4 14x y ( 7)( 1) x x 2 x 8x 7 ( 4)( 2) x x 2 x 6x 8
- 15. ( 6)( 5) x x 2 x 11x 30 ( 7)( 3) x x 2 x 10x 21 ( 9)( 3) x x 2 x 6x 27
- 16. ( 6)( 3) x x 2 x 3x 18 ( 1)( 8) x x 2 7 8 x x ( 2)( 7) x x 2 5 14 x x
- 17. Tie Breaker (3x + 2) (2x + 3) 6x2 + 13x + 6