Chapter 13 8 th Grade McDowell

Polynomials5/5 A real number, a variable, or a product and a real number and variable with whole number exponents An expression without addition, subtraction---can’t divide by a variable 5 xy/2 -112a 3m³n² monomial Examples monomialNot a monomial 7 - a xy/z 34 + b 4k - ³

Is the expression a monomial? c 2.7z/3 3.6ab² 4.4g/h y 6.7 No Yes No Yes You try

A monomial or the sum or difference of monomial(s) polynomial termThe monomials that make up a polynomial Polynomial# of termsExample Monomial1h, 3d/4, ¼p³ Binomial2w + 4, 3f – r² Trinomial3x² + 5x – 23 Polynomial1 or moreAll of the above

Name the polynomial 1.5c – 2 + a 2.56 – x x² + 2x 5.7p² 6.ab – a + b Trinomial Binomial Monomial Binomial Monomial trinomial You try

Plug and Chug Evaluating polynomials Evaluate the 3x for x = 5 3x 3(5) 15 Evaluate gh³ + 4g - ½h for g = 10, h = 4 gh³ + 4g - ½h (10)(4)³ + 4(10) - ½(4) (10)(64) + 4(10) - ½(4) Plug in the values Chug out the answer following PEMDASLR Plug in the values Chug out the answer following PEMDASLR

Evaluate the expression for a = 2, b = a + b² ab 3.a² - 2b a - 3b 5.ab² a You try

Adding and Subtracting Polynomials 5/6 Like terms have the same variable and exponent or no variable at all (4b² + 2b + 1) + (7b² + b – 3) Like terms Add like terms 11b² + b - 2 Vertical Method Find like terms

(2y² - 9y – 15) + (6y² + 8y – 11)Vertical Method Line up like terms 2y² - 9y – y² + 8y – 11 Combine like terms 2y² - 9y – y² + 8y – 11 8y² - 1y - 26

Simplify each sum using any method 1.(x² + 3x + 1) + (x² + x + 6) 2.(5x² + 3x + 7) + (7x – 2) 3.x 4 + 3x³ - x² + x – 2 + 7x³ + x² - 5x – 9 4.xy + 5x – 2y xy – 3x – 3y - 8 You Try

Remember the distributive property Subtraction A negative outside parenthesis belongs to everything inside the parenthesis Change subtraction to addition Change the sign of the 2 nd number

Change, Change, Go Vertical Method (-4x² + x – 1) – (x² - x + 8) Distribute the negative sign (-4x² + x – 1) + (-x² + x - 8) Find like terms (-4x² + x – 1) + (-x² + x - 8) Combine like terms -5x² + 2x - 9

x² - 3x – x - 4 Vertical Method Change, Change, Go Distribute the negative sign x² - 3x – x + 4 Combine like terms x² - 8x - 5 x² - 3x – x + 4

Find the difference 1.(ab – 4) – (3ab – 6) 2.(2x² + 3x – 7) – (x² - 6x – 9) 3.3x² + x x² + x y – 8 - 2y + 7