Name ____________ Polynomials A monomial is _______________________________ A polynomial is _______________________________ These are monomials 4x3 -7ab 1 y These are NOT monomials x 1 X2 1 5 y 2 -8 x2 + 4 2x2y n2 + 2n + 5 Circle the polynomials: X -x2 ½ 0.024 5/x x-2 2x+3y –4 8 A polynomial with 2 terms is a ____________________________ A polynomial with 3 terms is a ____________________________ A polynomial with more than 3 terms is a _____________________ Label each as M – monomial, B – binomial, T – trinomial, P – polynomial or X if it is not a polynomial: 7 + 4x – 1 x ___ 5n + 3 ___ 3x2 + 2x – 4 ___ 7 ___ 5 ___ 9 – 25x2 ___ 3x + 3y + 3z ___ 2x + y – z + 4 ___ m – 2m2 ___ m 3 ___ m2 ___ 2x ___ x + 4x2 + 2x3 ___ ___ 3 + 21 – 4x + 5 ___ 2a – b + 3c – d + 4e ___ 1 st 2 2 5 m ___ x – 2y + z - 2n ___ 3.152x The coefficient is _____________________________________ Identify the coefficient of each variable: 3x ___ -2x ___ 3x 4 ___ 257m ___ 7x 6 ___ 4x + 7 ___ 12 m ___ 3 7n3 ___ 42 – n ___ 3x2 ___ 7 – x2 ___ x + 7 ____ 3 - x + 4 ____ 5 5 – 3 x ___ x + 2 ___ 7 x – 5 ____ 2 2x + 8 ____ 5 x4 ___ -x5 n 5 ___ ___ The degree of a monomial is ________________________________ Find the degree of each monomial: 6n2 ___ 13x7y3 ___ k4m2n5 ___ 3m5n4 ___ 8a4b ___ 24 ___ -r3s6t ___ 7xy ___ 2x4y ___ 5x ___ -15 ___ mn ___ 5x7y3 ___ 8 ____ x2y 5 ____ 7x2y3z ___ -x5y7 ___ x xy9 ____ a6b3c4d2 ___ ____ The degree of a polynomial is __________________________ Find the degree of each polynomial: 4x6y3 - 2xy5 + 5xy ___ ___ ___ 3x3y5z2 + 2x2y2z2 – x4y3z ___ ___ ___ 9x4y – 2x3y – x2y4 ___ ___ ___ 5xy5 - 2x3y2 + 4x4y5 - 9x2y2 ___ ___ ___ ___ 2xy2 + 5x2y3 + 3xy ___ ___ ___ 9x4y6z2 + 6x7y5z + 4x5y6z3 + 3x8yz2 ___ ___ ___ ___ 6x2y – 3x4y – x3y4 ___ ___ ___ 8xy5 - 4x3y2 + 9x2y2 - 2x2y5 ___ ___ ___ ___ 3xy7 + 4x4y3 + 8xy ___ ___ ___ 2x5y7z2 + 7x8y5z + 3x4y8z3 + 3x9yz2 ___ ___ ___ ___ 7x8y – 3x6y – x3y5 ___ ___ ___ 7xy2 - 6x2y2 + 5x4y - 4x2y2 ___ ___ ___ ___ 2xy6 + 3x5y3 + 4x4y5 ___ ___ ___ 2x3y7z2 + 9x5y7z + 3x3y6z5 + 8x7yz3 ___ ___ ___ __ Writing Polynomials in or order 2x4y3 – 5x3y4 + 5x2 – x + 3 is written in descending order for the x variable. The term with the greatest exponent for x is written first. 5 – 3xy3 + 4x3y4 – 3x5y3 is written in ascending order for the x variable. The term with the lowest exponent for the x is written first. What is the exponent for x in the term 5? _______ Arrange each polynomial in descending order for the x variable: 4x4 + 4x7 + x2 + 2x3 ___________________________________ 3y + 4x5y2 – 4x2 + 5xy4 + 3x3 _____________________________ x + 3x5 + 4x3 + 5x2 + 6x7 – 2x4 ____________________________ - 14y + 7x2y3 – 10x3y2 – 14x7 ______________________________ Insert the term in the correct place for descending order according to the x: 3x4 5x5 + 2x3 + 7x + 1 2x x3 + 3x2 + 5 X3y7 x5 y + x4y + x2y3 x2y4 x3y2 + xy5 + xy 2x3 x4 + 5x2 + 9x 9x2 3x5 + 4x4 + 7 Like Terms are ________________________________________________ Find 3 like terms in each row. 1. 6x 3y x3 x 3 x 2. 8m2 -m 8mn 8 m 3. 5xy 4yz 3zy 2yz z 4. 6ab 7ac 8bc 9ab 10ba 5. 6x2 3x3 4x3 5x x3 6. x2y xy2 2x2y2 3x2y 5yx2 7. 3x 3w x3 x 3 x 8. 4bvm 5mvb 6vmb 7mv 8mb 9. 7x 8x 9x 10x x4 4 10. 4x2y3z 4 3 3xy2z3 4 8x3y2z 5x2y3z 6zx2y3 Combining Polynomials 1. (x + 4) + (x – 3) (x - 5) – (2x + 4) _____________ _____________ _____________ _____________ 3. (x2+ 5) – (2x –3) 4. (5x2 –2x + 5) + (3x –7 + 2x2) __________________ ___________________ __________________ ____________________ 5. (x2 + 5) + (2 – 3x + 4x2) 7. 2. 6. (5x3 – 8x2 + 1) – (4x + 5 – x3 + 2x2) ___________________ _____________________________ ___________________ ______________________________ (7x - 8) + (4x – 3) 8. (8 - x) – (x + 4) __________________ _____________________ __________________ ______________________ 9. (6x2+ 2x ) – (2x – 3) 10. (3x2 + 7x - 5) + (3x – 7 + 5x2) __________________ _______________________ __________________ _______________________