document.write( "Question 56810This question is from textbook
\n" ); document.write( ": the degree 3 polynomial f(x) with real coefficients and leading coefficents 1, has 4 and 3+i among its roots. express f(x) as a product of linear and quadratic polynomials with real coefficents. \n" ); document.write( "

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the degree 3 polynomial f(x) with real coefficients and leading coefficents 1, has 4 and 3+i among its roots. express f(x) as a product of linear and quadratic polynomials with real coefficents.
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\n" ); document.write( "Let (x-4) be one factor:
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\n" ); document.write( "Find x = 3 + i
\n" ); document.write( "x - 3 = i
\n" ); document.write( "Square both sides:
\n" ); document.write( "(x-3)^2 = i^2
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\n" ); document.write( "FOIL (x-3)^2 and i^2 = -1
\n" ); document.write( "x^2 - 6x + 9 = -1
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\n" ); document.write( "x^2 - 6x + 9 + 1 = 0
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\n" ); document.write( "x^2 - 6x + 10 = 0 is the quadratic polynomial
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\n" ); document.write( "Mult by the other factor (x-4)
\n" ); document.write( "(x-4)*(x^2 - 6x + 10) = x^3 - 10x^2 + 34x - 40, a 3rd degree polynomial
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