X 4 5 x 2 4 math 17 inst of mathematics polynomials

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x 4 - 5 x 2 + 4 Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 29 / 30
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Factoring Polynomials Illustration: Factor x 4 - 5 x 2 + 4 . x 4 - 5 x 2 + 4 = x 4 - 4 x 2 + 4 - x 2 Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 29 / 30
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Factoring Polynomials Illustration: Factor x 4 - 5 x 2 + 4 . x 4 - 5 x 2 + 4 = x 4 - 4 x 2 + 4 - x 2 Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 29 / 30
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Factoring Polynomials Illustration: Factor x 4 - 5 x 2 + 4 . x 4 - 5 x 2 + 4 = x 4 - 4 x 2 + 4 - x 2 = ( x - 2) 2 - x 2 Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 29 / 30
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Factoring Polynomials Illustration: Factor x 4 - 5 x 2 + 4 . x 4 - 5 x 2 + 4 = x 4 - 4 x 2 + 4 - x 2 = ( x - 2) 2 - x 2 = ( x 2 + x - 2)( x 2 - x - 2) Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 29 / 30
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Factoring Polynomials Illustration: Factor x 4 - 5 x 2 + 4 . x 4 - 5 x 2 + 4 = x 4 - 4 x 2 + 4 - x 2 = ( x - 2) 2 - x 2 = ( x 2 + x - 2 )( x 2 - x - 2) Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 29 / 30
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Factoring Polynomials Illustration: Factor x 4 - 5 x 2 + 4 . x 4 - 5 x 2 + 4 = x 4 - 4 x 2 + 4 - x 2 = ( x - 2) 2 - x 2 = ( x 2 + x - 2 )( x 2 - x - 2 ) Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 29 / 30
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Factoring Polynomials Illustration: Factor x 4 - 5 x 2 + 4 . x 4 - 5 x 2 + 4 = x 4 - 4 x 2 + 4 - x 2 = ( x - 2) 2 - x 2 = ( x 2 + x - 2 )( x 2 - x - 2 ) = ( x + 2)( x - 1)( x - 2)( x + 1) Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 29 / 30
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Factoring Polynomials Illustration: Factor x 4 - 5 x 2 + 4 . x 4 - 5 x 2 + 4 = x 4 - 4 x 2 + 4 - x 2 = ( x - 2) 2 - x 2 = ( x 2 + x - 2 )( x 2 - x - 2 ) = ( x + 2)( x - 1)( x - 2)( x + 1) x 4 - 5 x 2 + 4 Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 29 / 30
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Factoring Polynomials Illustration: Factor x 4 - 5 x 2 + 4 . x 4 - 5 x 2 + 4 = x 4 - 4 x 2 + 4 - x 2 = ( x - 2) 2 - x 2 = ( x 2 + x - 2 )( x 2 - x - 2 ) = ( x + 2)( x - 1)( x - 2)( x + 1) x 4 - 5 x 2 + 4 = ( x 2 - 4)( x 2 - 1) Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 29 / 30
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Factoring Polynomials Illustration: Factor x 4 - 5 x 2 + 4 . x 4 - 5 x 2 + 4 = x 4 - 4 x 2 + 4 - x 2 = ( x - 2) 2 - x 2 = ( x 2 + x - 2 )( x 2 - x - 2 ) = ( x + 2)( x - 1)( x - 2)( x + 1) x 4 - 5 x 2 + 4 = ( x 2 - 4 )( x 2 - 1) Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 29 / 30
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Factoring Polynomials Illustration: Factor x 4 - 5 x 2 + 4 . x 4 - 5 x 2 + 4 = x 4 - 4 x 2 + 4 - x 2 = ( x - 2) 2 - x 2 = ( x 2 + x - 2 )( x 2 - x - 2 ) = ( x + 2)( x - 1)( x - 2)( x + 1) x 4 - 5 x 2 + 4 = ( x 2 - 4 )( x 2 - 1 ) Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 29 / 30
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Factoring Polynomials Illustration: Factor x 4 - 5 x 2 + 4 . x 4 - 5 x 2 + 4 = x 4 - 4 x 2 + 4 - x 2 = ( x - 2) 2 - x 2 = ( x 2 + x - 2 )( x 2 - x - 2 ) = ( x + 2)( x - 1)( x - 2)( x + 1) x 4 - 5 x 2 + 4 = ( x 2 - 4 )( x 2 - 1 ) = ( x - 2)( x + 2)( x + 1)( x - 1) Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 29 / 30
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Factoring Polynomials Illustration: Factor x 4 - 5 x 2 + 4 . 1. Completing the Square x 4 - 5 x 2 + 4 = x 4 - 4 x 2 + 4 - x 2 = ( x - 2) 2 - x 2 = ( x 2 + x - 2 )( x 2 - x - 2 ) = ( x + 2)( x - 1)( x - 2)( x + 1) x 4 - 5 x 2 + 4 = ( x 2 - 4 )( x 2 - 1 ) = ( x - 2)( x + 2)( x + 1)( x - 1) Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 29 / 30
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Factoring Polynomials Illustration: Factor x 4 - 5 x 2 + 4 .
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