Give the factorization of the equation x^7 + 2x^6 + 6x^5 + 3x^4 +7x^3 + 5x + 4 t

Question

Give the factorization of the equation x^7 + 2x^6 + 6x^5 + 3x^4 +7x^3 + 5x + 4 that results from Horner's method. Show the result value from each pass of horners method using input x = 4 with the given polynomial

Explanation / Answer

x^7 + 2x^6 + 6x^5 + 3x^4 +7x^3 + 5x + 4 4 + x(5 + x^2(7 + x(3 + x(6 + x(2 + x))))) when x = 4 4 + x(5 + x^2(7 + x(3 + x(6 + x(2 + x))))) => 4 + 4(5 + 4^2(7 + 4(3 + 4(6 + 4(2 + 4))))) => 4 + 4(5 + 4^2(7 + 4(3 + 4(6 + 4(6))))) => 4 + 4(5 + 4^2(7 + 4(3 + 4(6 + 24)))) => 4 + 4(5 + 4^2(7 + 4(3 + 4(30)))) => 4 + 4(5 + 4^2(7 + 4(3 + 120))) => 4 + 4(5 + 4^2(7 + 4(123))) => 4 + 4(5 + 4^2(7 + 492)) => 4 + 4(5 + 4^2(499)) => 4 + 4(5 + 16(499)) => 4 + 4(5 + 7984) => 4 + 4(7989) => 4 + 31956 => 31960

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