polynomials - missmccormickscience.files.wordpress.com€¦ · polynomials for an expression to be...
TRANSCRIPT
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PolynomialsMath 9
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Polynomials ActivityMath 9
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Your Task #1
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Your Task #2
Create 5 of your own expressions and record them on a piece of paper. Use at least 2 variables.
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Your Task #3
Trade with somebody else and have them simplify the 5 expressions that you created. Record on your paper.
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Your Task #4
What do you think a polynomial is?
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Introduction to PolynomialsMath 9
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Review
● A polynomial is one term or the sum or difference of terms whose variables have whole-number exponents.
● Polynomial comes from poly- (meaning "many") and -nomial (in this case meaning "term") ... so it really means "many terms".
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Polynomials
For an expression to be a polynomial term, it must contain no square roots of variables,
no fractional or negative powers on the variables, and no variables in the denominators
of any fractions. Here are some examples:
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Degree
The term with the greatest exponent determines the degree of the polynomial.
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Examples
Polynomial Constant Coefficient (s) Variable (s) Degree
x + 4 4 1 x 1
-2x - 8
3x2 + 3y
2y2 + 4y + 6
22
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Simplifying Polynomials
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Example
Miss McCormick has a basket of fruit in each hand. One basket contains 2 apples, 6 oranges, and 8 mangoes. The other basket contains 3 apples, 2 oranges, and 2 mangoes. Model and add the fruit using polynomials.
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Examples
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Example
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Assignment
Page 214
#’s 4, 5, 6, 9, 10, 20
AND
Page 222
#’s 6, 7, 12, 13, 22
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Adding PolynomialsMath 9
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Review
To add polynomials, we combine the like terms. There are two ways to do this.
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Examples
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Examples
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Example
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Example
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Assignment
Page 228
#’s 8, 12, 15, 17
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Subtracting PolynomialsMath 9
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Review
When subtracting integers, we always combine the middle signs, then add or subtract where appropriate.
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Examples
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Examples with Polynomials
Next step:
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Recall
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Subtracting Polynomials
(a + 1) – (-3a + 2) Distribute to both terms & remove brackets
= (a + 1) + 3a – 2 Change signs
= a + 1 + 3a – 2 Re-arrange like terms
= a +3a +1 – 2 Combine like terms
= 4a – 1
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Examples
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Assignment
Page 234
#’s 5, 8, 10, 12, 13, 15 (a, c, e)
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Multiplying and Dividing Polynomials by a ConstantMath 9
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Review
● Remember that when numbers and letters are side by side it indicates multiplication
● 4nm means 4 x n x m● In a multiplication, switching the order of numbers and
variables does not change the product ● 4nm is the same as nm4 or n4m or m4n
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Examples
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Examples
Determine the product.
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Dividing
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Examples
Determine the quotient.
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Examples
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Assignment
Page 246
#’s 7 (a), 8 (a), 12, 15, 16, 19 (a), 22 (a, c, e)
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Multiplying and Dividing Polynomials by a MonomialMath 9
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Review
When multiplying polynomials, each term from one polynomial must be multiplied by each term of the other polynomial.
When multiplying monomials, use the product rule for exponents:
xm × xn = xm + n
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Examples
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Review
When dividing polynomials, each term in the numerator must be divided by each term in the denominator.
When dividing monomials, use the quotient rule for exponents:
xm ÷ xn = xm - n
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Examples
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Examples
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Assignment
Page 255
#’s 9 (a), 10 (a), 12, 14, 16, 22
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Evaluating PolynomialsMath 9
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Evaluating Polynomials Example
Evaluate the polynomial if x = 2.
6x2 + 3x + 6
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Evaluating Polynomials Example
Evaluate the polynomial if x = 2 and y = 4.
20 - 2xy
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Polynomial Review StationsMath 9
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Polynomial StationsStation One - Polynomial Jeopardy (NEED A COMPUTER)
Station Two - Polynomial Identification (NEED TWO COMPUTERS)
Station Three - Evaluate the Polynomial (NEED TWO COMPUTERS)
Station Four - Polynomials Battleship (NEED TWO COMPUTERS)
Station Five - A Dicey Polynomial Situation (NEED TWO DIE, POLYNOMIAL CARDS, AND RECORDING SHEETS)
Station Six - Polynomial Bullseye (NEED A BULLSEYE SHEET PER STUDENT)
Station Seven - Polynomial Stick Sort (NEED TWO SETS OF POLYNOMIAL POPSICLE STICKS)
Station Eight - WhoDunnit Combining Like Terms Mystery (NEED ONE BOOKLET PER STUDENT)
Station Nine - Adding and Subtracting Polynomials Race (NEED ONE SHEET PER STUDENT)
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Review
Page 259-261
#’s 2, 3, 5, 12, 15, 19, 22, 23, 26, 28
Practice Test Page 262