Lesson 10.1: Adding/subtracting Polynomials Monomial: An expression with one term Ex. a) 2 b) 3x c)-12x2y3 Binomial: An expression with two terms Ex. a) x + 4 b) 2xy + 7ab Trinomial: An expression with three terms Ex. 7x2 + 5x - 7 Polynomial: An expression that is the sum of terms (one or more terms) Ex. 5x + 7y + 15xy – 11z

Standard Form: Polynomials written in decreasing order of the variable Standard Form NOT Standard form 3x2 – 2x + 7 7 + 3x2 –2x 2x3y +4x2y2 – 3xy3 – 11 4x2y2 – 11 + 2x3y –3xy3 Coefficient: Number multiplied by a variable in a term Ex. 3xy coefficient is 3 Leading coefficient: coefficient of first term of a polynomial written in standard form. Ex. -5x2 + 7x –2 L.C. = -5

Constant: a term with no variables Ex. 8 Examples: Write in standard form, determine coefficients, leading coefficient, and constant 4 – x + 2x3 2) -9x + 2 3) 2x3 – x + 4 Coeff= 2, -1 LC = 2 Constant = 4 Coeff= -9, 2 LC = -9 Constant = 2 LC = 2 Constant = -7 2x3 + 5x2 – 3x -7 Coeff= 2m 5m –3m -7

Degree of a term: exponent of variable Degree of polynomial: largest degree of the terms Can classify polynomial by terms (monomial, binomial, trinomial, polynomial) or by degree. Degree classifications Degree Classification Example 0 Constant 9 1 Linear x + 7 2 Quadratic x2 – 5x + 2 3 Cubic 3x3 - 1 4 Quartic -5x4 –x3 –7x2+2x-3

Classify by degree and number of terms. -5 2) 3) 4) Monomial Constant Monomial Linear Polynomial Cubic Binomial Quadratic

To add/subtract polynomials: - Use commutative and associative props. to group like terms - Combine like terms **** Remember to change subtraction to adding the opposite.

-8x3 +(-9x2)+ 0x + 2 0x3 + 8x2 + 2x + 4 + -3x3 + 4x2 + 0x + -1 -11x3 + 3x2 + 2x +5

Homework p. 580, #19-30 all,#32-62 evens, #63-64