prcreva3

prcreva3 - 3 3 2 2 + = +-+ The process of expressing a...

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A.3 Polynomials
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A monomial in one variable is the product of a constant and a variable raised to a nonnegative integer power. Thus, a monomial is of the form ax k where a is a constant, x is a variable, and k > 0 is an integer.
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Monomial Coefficient Degree 3 2 9 4 x x - 3 4 2 1 -9 0
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A polynomial in one variable is an algebraic expression of the form
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Coefficients: 5, 0, -3, 1, -7 Degree: 4
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Adding and Subtracting Polynomials
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( 29 ( 29 2 8 1 3 5 2 3 2 3 x x x x x - + + + - - ( 29 ( 29 ( 29 = + - + - + - 2 3 8 5 1 2 3 3 2 x x x x x = - + - 5 3 1 3 2 x x x ( 29 ( 29 2 8 1 3 5 2 3 2 3 x x x x x - + + - - - = - + + - + + 2 8 1 3 5 2 3 2 3 x x x x x ( 29 ( 29 ( 29 = - - + + + + 2 3 8 5 1 2 3 3 2 x x x x x = - - + + x x x 3 2 13 3
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Multiplying Polynomials
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( ax + b )( cx + d ) First Outer Inner Last FOIL ( ax + b )( cx + d ) = ax ( cx ) + ax ( d ) + b ( cx ) + b ( d ) = acx + ( ad+bc ) x + bd
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Special Products Difference of Two Squares ( 29 ( 29 x a x a x a - + = - 2 2 Squares of Binomials, or Perfect Squares ( 29 ( 29 x a x ax a x a x ax a + = + + - = - + 2 2 2 2 2 2 2 2
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Special Products Miscellaneous Trinomials ( 29 ( 29 ( 29 x a x b x a b x ab + + = + + + 2 ( 29 ( 29 ( 29 ax b cx d acx ad bc x bd + + = + + + 2 Cubes of Binomials, or Perfect Cubes ( 29 ( 29 x a x ax a x a x a x ax a x a + = + + + - = - + - 3 3 2 2 3 3 3 2 2 3 3 3 3 3
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Special Products Difference of Two Cubes ( 29 ( 29 x a x a x ax a 3 3 2 2 - = - + + Sum of Two Cubes ( 29 ( 29 x a x a x ax a
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Unformatted text preview: 3 3 2 2 + = +-+ The process of expressing a polynomial as a product of other polynomials is called factoring . ( 29 ( 29 2 3 4 2 5 12 2 x x x x-+ = +-Factor out the common factor of: 10 x x x 3 2 2 8 + + Factor completely: 9 x 2 64-( 29 9 64 3 8 2 2 2 x x-=-( 29 ( 29 = +-3 8 3 8 x x x 3 64 + ( 29 ( 29 = +-+ x x x 4 4 16 2 Factor completely: x 4 1-( 29 ( 29 = +-x x 2 2 1 1 ( 29 ( 29 ( 29 = + +-x x x 2 1 1 1 Factor the following polynomial completely: Factor the trinomial: x x 2 11 18 + + Look for factors of 18 whose sum is 11. ( 29 ( 29 x x x x 2 11 18 2 9 + + = + + Factor the trinomial: x x 2 3 10--Factors of -10 Sum 10, -1 5, -2-5, 2-10, 1 9 3-3-9 ( 29 ( 29 x x x x 2 3 10 5 2--=-+ Factor completely: 3 7 6 2 x x--( 29 ( 29 3 7 6 3 2 x x x x--=...
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prcreva3 - 3 3 2 2 + = +-+ The process of expressing a...

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