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Section 4.3

# Section 4.3 - f-2 using synthetic division The remainder is...

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Section 4.3 Polynomial Division; The Remainder and Factor Theorems Recall, a factor divides an expression without a remainder. To see if x - 1 is a factor of x 4 - 1 divide x 4 - 1 by x - 1. If the remainder is zero then x - 1 is a factor of x 4 - 1. We may use polynomial long division or synthetic division. For both polynomial long division and synthetic division, add 0x k for any powers of x missing from the polynomial you are dividing. k is the missing power. Polynomial Long Division ( x 4 - 1 ) ÷ ( x - 1 ) = Is x - 5 a factor of x 3 - 9x 2 + 15 x + 25 ? Synthetic Divison ( x 4 - 1 ) ÷ ( x - 1 ) = Is x - 5 a factor of x 3 - 9x 2 + 15 x + 25 Remainder Theorem Let f(x) be a polynomial function. If f(x) is divided by x – c, then the remainder is equal to f(c). Given f(x ) = x 3 - 6x

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Unformatted text preview: f(-2) using synthetic division . The remainder is so f(-2) = . Factor Theorem Let f(x) be a polynomial function. If f(c) = 0, then x -c is a factor of f(x). The remainder is f(c) so if the remainder is zero, then x -c is a factor of f(x). The factor theorem is useful in factoring polynomials to solve polynomial equations and find zeros of polynomial functions. Factor the polynomial function f(x). Then solve the equation f(x) = 0. f(x) = x 4-4x 3-7x 2 + 34x -24 The solutions to f(x) = 0 are the zeros of the polynomial f(x). Using synthetic division, determine whether 2 is a zero of f(x) = 3x 3 + 5x 2-6x + 18. Using synthetic division, determine whether -2i is a zero of g(x) x 3-4x 2 + 4x -16....
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