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Transcript of Polynomials
4) 56 Polynomials *Polynomial: Is a monomial or a sum of monomials.(Ex. 3n +2d + 3j +2c + 3c) Degree - Example *Monomial is a number, variable, or a product of a number and 1 or more variable(s). Definitions: *Binomial: The sum of two monomials.
(Ex. 3b + 6a) *Trinomial: The sum of three monomials.
(Ex. c + 2a + 3t) *Degree of a Polynomial: The greatest degree (exponent) of any term in the polynomial. Ex. 1 *Degrees are always in a descending order.
Ex.: -4x y + 3x + 5 2 2 2 4 2 *4 is the largest exponent so it's the degree of the polynomial Ex. 2 9y 1 *If there is no exponent written then it is to the power of one 6h - h + p + p 4 3 2 *In one term you add all exponents for the total degree Adding Polynomials-Example *To add polynomials line up the like terms and add, or group like terms together. Watch... Ex. 1 (4x - 5x + 9) + (3x + 4x + 3)
Way 1: Horizontal
(4x + 4x ) + (-5x + 3x) + (9 + 3)
=8x - 2x + 12 2 2 2 2 Way 2: Vertical
4x - 5x + 9 2 + 4x + 3x+ +3 2 8x - 2x + 12 2 2 *Group the like terms. *Add like terms * The polynomials are in descending degree order. * Align like terms and add. Subtracting Polynomials - Example Ex. 1 (4n + 7n + 5n) - (3n + 6n)
Way 1: Horizontal 3 2 3 Way 2: Vertical
7n + 4n + 5n - 3n + 6n 3 2 3 *Align like terms and subtract 7n + n - n 3 2 Multiplying polynomials by a monomial Multiplying polynomials not
7h + 3p + 67 3 7n + (4n - 3n ) + (5n - 6n) 2 3 3 *Group like terms = n + 7n - n 2 3 Ex. 1 -4x(2x - 6x + 15) Way 1: Horizontal -4x(2x) - -4x(6x) + -4x(15) =-8x + 24x - 60x Way 2: Vertical (2x - 6x + 15) = 16x - 60x x -4x 16x - 60x *Monomial *Polynomial "Foil" Method (x + 4)(x - 6) = x(x - 6) + 4(x - 6) *Distributive property =x - 6x + 4x - 24 2 *Solve =x - 2x - 24 2 *Simplify Ex. 1 Steps: F - First terms
O - Outer terms
I - Inner terms
L - Last terms
(x + 4)(x - 3) Outer Inner First Last *This makes it easier to multiply polynomials. Any questions about Degree, Subtracting, Adding, Multiplying polynomials, or the FOIL method? *Distributive property Steps: *Solve and simplify *Solve (descending egree) Steps: *Complete the homework worsheet. 1/11/13 *Once you multiply each term according to FOIL, write out the equation and simplify You try:
(2x + 8)(x - 2) You try:
(x + 4)(2x - 3) You try:
-2x(x + 10) You try:
1) (2x - 5) - (x + 4)
2) (3x + 5) + (x + 2) Answers:
4) Yes * Rearrange degrees in descending order. = n + 7n - n 3 2 Answers:
1) (x - 9)
2) (4x + 7) Answer:
-2x - 20x 2 2 2 2 2 Answer:
2x + 5x - 12 2 Answer:
2x + 4x - 16 2