algebraic extensions of order of operations to polynomials
TRANSCRIPT
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Algebraic Extensions of Order of
Operations
to Polynomials
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Purpose:
1.) Introduce algebraic expressions and their meaning.
2.) Evaluate algebraic expressions.
3.) Introduce polynomials.
4.) Learn the vocabulary of polynomials.
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Algebraic expressions – are expressions involving variable, constant or a combination of variable and constant.
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TABLE 1 (Values of Expressions)
Expression/x 1 2 3 4 5
x + 5 8
7x 14
7x + 5
x2+ 7x + 5
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TABLE 1 (Values of Expressions) - Answers
Expression/x 1 2 3 4 5
x + 5 6 7 8 9 10
7x 7 14 21 28 35
7x + 5 12 19 26 33 40
x2+ 7x + 5 13 23 35 49 65
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TABLE 2 (Operations on x in Expressions)
Expression Operations in xx + 5 Add 5
7x7x + 5
x2 + 7x + 54x - 34x3
3x2 + 4
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TABLE 2 (Operations on x in Expressions)- Answers
Expression Operations in xx + 5 Add 5
7x Multiply by 7
7x + 5 Multiply by 7, add 5 to the product
x2 + 7x + 5Square input, multiply input by 7, add the square and the product, add 5 to
the sum
4x - 3 Multiply by 4, subtract 3 from the product
4x3 Cube input, multiply the cube by 4
3x2 + 4 Square input, multiply the square by 3, add 4 to the product.
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Draw a relationship machine for each of the following expressions:
a. 7x + 5
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Draw a relationship machine for each of the following expressions:
a. 7x + 5x
Multiply by 7Add 5 to the product
7x + 5
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Draw a relationship machine for each of the following expressions:
b. 3x2 + 4
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Draw a relationship machine for each of the following expressions:
b. 3x2 + 4x
Square inputMultiply square by 3Add 4 to the product
3x2 + 4
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Draw a relationship machine for each of the following expressions:
c. 4x – 3
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Draw a relationship machine for each of the following expressions:
c. 4x – 3x
Multiply by 4Subtract 3 from the product
4x – 3
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Draw a relationship machine for each of the following expressions:
d. 5x2 + 8
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Draw a relationship machine for each of the following expressions:
d. 5x2 + 8x
Square inputMultiply square by 5Add 8 to the product
5x2 + 8
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Vocabulary of Polynomials
A polynomial is a mathematical expression consisting of a sum of polynomial terms.
A polynomial term is a constant or a product of a constant and one or more variables raised to positive integral power.
A constant is a number. For example 5 is a constant, but x and 5x are not constants.
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Vocabulary of Polynomials
A monomial is a polynomial with exactly one term.
A binomial is a polynomial with exactly two terms.
A trinomial is a polynomial with exactly three terms.
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Vocabulary of Polynomials
A numerical coefficient of a term is the constant factor of the term.
A constant term in a polynomial is the term that contains no variables. If there is no such term, then the constant term is 0.
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Vocabulary of Polynomials
A linear polynomial with only one variable is a polynomial in which the highest power on the variable is one. The one is often implied than written.
A quadratic polynomial with only one variable is a polynomial in which the highest power on the variable is two.
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Vocabulary of Polynomials
The degree of the polynomial with only one variable is the highest power on the variable.
Linear polynomials have a degree of 1.
Quadratic polynomials have a degree of 2.
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Direction: Write YES if it is an algebraic expression or a polynomial and NO if it is
not.
Given Algebraic Expression Polynomial
1.) 4
2.)
3.) 4x +
4.) twice x
5.)
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Direction: Write YES if it is an algebraic expression or a polynomial and NO if it is not. -
Answers
Given Algebraic Expression Polynomial
1.) YES NO
2.) YES NO
3.) 4x + YES YES
4.) twice x NO NO
5.) YES NO