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Adding and subtracting Polynomials Lesson 8-1 TOPIC IX: Quadratic Equations and Functions
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What does each prefix mean? mono one bi two tri three
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Monomial is a real number, a variable, or a product of a real number and one or more variables with whole- number exponent. Here are some examples of monomials
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What about poly? one or more A polynomial is a monomial or a sum/difference of monomials. Important Note!! An expression is not a polynomial if there is a variable in the denominator.
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You can name a polynomial based on its degree or the number of monomials it contains
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State whether each expression is a polynomial. If it is, identify it. 1) 7y - 3x + 4 trinomial 2) 10x 3 yz 2 monomial 3) not a polynomial
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Which polynomial is represented by X2X2 1 1 X X X 1.x 2 + x + 1 2.x 2 + x + 2 3.x 2 + 2x + 2 4.x 2 + 3x + 2 5.I’ve got no idea!
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The degree of a monomial is the sum of the exponents of the variables. Find the degree of each monomial. 1) 5x 2 2 2)4a 4 b 3 c 8 3)-3 0
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To find the degree of a polynomial, find the largest degree of the terms. 1) 8x 2 - 2x + 7 Degrees: 2 1 0 Which is biggest? 2) y 7 + 6y 4 + 3x 4 m 4 Degrees: 7 4 8 2 is the degree! 8 is the degree!
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Find the degree of x 5 – x 3 y 2 + 4 1.0 2.2 3.3 4.5 5.10
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A polynomial is normally put in ascending or descending order. What is ascending order? Going from small to big exponents. What is descending order? Going from big to small exponents.
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Means that the degrees of its monomial term decrease from left to right
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Put in descending order: 1)8x - 3x 2 + x 4 - 4 x 4 - 3x 2 + 8x - 4 2) Put in descending order in terms of x: 12x 2 y 3 - 6x 3 y 2 + 3y - 2x -6x 3 y 2 + 12x 2 y 3 - 2x + 3y
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3) Put in ascending order in terms of y: 12x 2 y 3 - 6x 3 y 2 + 3y - 2x -2x + 3y - 6x 3 y 2 + 12x 2 y 3 4)Put in ascending order: 5a 3 - 3 + 2a - a 2 -3 + 2a - a 2 + 5a 3
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Write in ascending order in terms of y: x 4 – x 3 y 2 + 4xy – 2x 2 y 3 1.x 4 + 4xy – x 3 y 2 – 2x 2 y 3 2.– 2x 2 y 3 – x 3 y 2 + 4xy + x 4 3.x 4 – x 3 y 2 – 2x 2 y 3 + 4xy 4.4xy – 2x 2 y 3 – x 3 y 2 + x 4
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You can add and subtract monomial by adding and subtracting like terms. Examples:
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Degree of each monomial Degree of each monomial
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You can add polynomials by adding like terms Line up like terms then add the coefficients Method 1 – Add vertically Method 2 – Add horizontally Group like terms then add the coefficients
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Recall that subtraction means to add the opposite. So when you subtract a polynomial, change each of the term to its opposite. Then add the coefficients Line up like terms Method 1 – Subtract vertically Then add the opposite of each term in the polynomial being subtracted
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Method 2 – Subtract horizontally Write the opposite of each term in the polynomial being subtracted Group like term Simplify
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1. Add the following polynomials: (9y - 7x + 15a) + (-3y + 8x - 8a) Group your like terms. (9y - 3y) + (- 7x + 8x) + (15a - 8a) = 6y + x + 7a Examples:
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Combine your like terms. (3a 2 ) + (3ab + 4ab) + (6b 2 - b 2 ) 3a 2 + 7ab + 5b 2 2. Add the following polynomials: (3a 2 + 3ab - b 2 ) + (4ab + 6b 2 )
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Add the polynomials. + X2X2 11 X X XY Y Y Y Y 111 X Y Y Y 1 11 1.x 2 + 3x + 7y + xy + 8 2.x 2 + 4y + 2x + 3 3.3x + 7y + 8 4.x 2 + 11xy + 8
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Line up your like terms. 4x 2 - 2xy + 3y 2 +-3x 2 - xy + 2y 2 _________________________ x 2 - 3xy + 5y 2 3. Add the following polynomials using column form (vertically): (4x 2 - 2xy + 3y 2 ) + (-3x 2 - xy + 2y 2 )
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Rewrite subtraction as adding the opposite. 9y - 7x + 15a + 3y - 8x + 8a Group the like terms. 9y + 3y -7x - 8x + 8a +15a 12y - 15x + 23a 4. Subtract the following polynomials: (9y - 7x + 15a) - (-3y + 8x - 8a)
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Rewrite subtraction as adding the opposite. (7a - 10b) + (- 3a - 4b) Group the like terms. 7a - 3a - 10b - 4b 4a - 14b 5. Subtract the following polynomials: (7a - 10b) - (3a + 4b)
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Line up your like terms and add the opposite 4x 2 - 2xy + 3y 2 + (+ 3x 2 + xy - 2y 2 ) 7x 2 - xy + y 2 6. Subtract the following polynomials using column form: (4x 2 - 2xy + 3y 2 ) - (-3x 2 - xy + 2y 2 )
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Find the sum or difference. (5a – 3b) + (2a + 6b) 1.3a – 9b 2.3a + 3b 3.7a + 3b 4.7a – 3b
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Find the sum or difference. (5a – 3b) – (2a + 6b) 1.3a – 9b 2.3a + 3b 3.7a + 3b 4.7a – 9b
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