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Factoring Polynomials - Math

Factoring PolynomialsAny natural number that is greater than 1 can be factored into a productof prime numbers. For example 20 = (2)(2)(5) and 30 = (2)(3)(5).In this chapter we ll learn an analogous way to factor Theorem of AlgebraAmonicpolynomial is a polynomial whose leading coe cient equals 1. Sox4 2x3+5x 7ismonic,andx 2ismonic,but3x2 following result tells us how to factor Polynomials . It essentially tellsus what the prime Polynomials are:Any polynomial is the product of a real number,and a collection of monic quadratic Polynomials thatdo not have roots, and of monic linear result is called theFundamental Theorem of Algebra.

Example. The discriminant of 4x 22x+2 equals (2) 4(4)(2) = 432 = 228, a negative number. Therefore, 4x 2x +2hasnoroots, anditis completely factored as 4(x2 1 2x+ 1 2). 2Roots.If the quadratic polynomial ax2 + bx + c has 2 roots, we can name them ↵1 and ↵2. Roots give linear factors, so we know that (x ↵1) 159

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Second Order Linear Differential Equations - Math

www.math.utah.edu

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www.math.utah.edu

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