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Polynomials Algebra I Remember: Monomials are separated by______ or ______ signs. Monomial = One term – A number, a variable, or a product of numbers and variables. Binomial = Two terms – 2 monomials separated by a + or – sign. Trinomial = Three terms – 3 monomials separated by + or – signs. Identity as a monomial, binomial, trinomial 1) 2) 3) 4) 5) 6) 5x2 4abc 3x + 2 3x2 – 8xy a2 + 2ab + b2 5x2 – 2x + 7 1) 2) 3) 4) 5) 6) Monomial Monomial Binomial Binomial Trinomial Trinomial Remember: Monomials are separated by______ or ______ signs. To find the degree of a monomial, add the exponents on the variables (from each monomial), then see which one has the largest sum. 7) 3x 5 2 2 0 Do not add across a “+” or “-” sign!!!! 8) y y 3x m 7 7 6 6 4 4 4+4=8 7) Largest number is 2 (degree is 2) 8) Largest sum is 8 (degree is 8) 9) x x y z z 5 5 3 6 2 5+3+6=14 The largest number (sum) is 14, so the degree of this trinomial is 14 Place in ascending order according to (x) 10) 5x x 4 x 2 2 3 2 x 5x 4x 2 3 Ascending means to go from least to greatest Remember to bring along sign that is in front of number Now which terms variable has the smallest exponent? Place in descending order according to (y) 11) 24 x y 12 x y 6 x 2 3 2 4 12x y 24x y 6x 3 2 2 4 Descending means to go from greatest to least Remember to bring along sign that is in front of number Now which terms variable has the largest exponent for “y”? REMEMBER – look at the exponents on each terms variable, If the term doesn’t have a variable, it’s degree is ZERO. 12) Write each polynomial in descending (going down) order and give the degree. 2 x 3x 3x 2 2 5 3x 2x 2 3x 2 5 5 2 1 Largest EXPONENT is 5, therefore the degree is 5. 0 2 3x 2 x 6 4 3x 2x 2 6 6 4 4 Largest EXPONENT is 6, therefore The degree is 6. 0 13) Evaluate when x = 2 and y = 3. X2 - 7xy + y2 2 7(2)(3) 3 4 42 9 2 29 2