document.write( "Question 54069This question is from textbook Algebra and Trigonometry
\n" ); document.write( ": Please help me with this problem:
\n" ); document.write( "The degree three polynomial f(x) with real coefficients and leading coefficient 1, has 4 and 3 + i among its roots. Express f(x) as a product of linear and quadratic polynomials with real coefficients. \n" ); document.write( "
Algebra.Com's Answer #36323 by stanbon(75887)\"\" \"About 
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The degree three polynomial f(x) with real coefficients and leading coefficient 1, has 4 and 3 + i among its roots. Express f(x) as a product of linear and quadratic polynomials with real coefficients.
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\n" ); document.write( "Since the coefficients are real, and since 3+i is a root, 3-1 must be
\n" ); document.write( "a root.
\n" ); document.write( "so the polynomial has factors: (x-4),(x-(3+i)),(x-(3-i))
\n" ); document.write( "f(x) is the product of these three factors.
\n" ); document.write( "f(x)= (x-4)((x-3)-i)((x-3)+i)
\n" ); document.write( "f(x)= (x-4)((x-3)^2-i^2)
\n" ); document.write( "f(x)= (x-4)(x^2-6x+9+1}
\n" ); document.write( "f(x)= (x-4)(x^2-6x+10)
\n" ); document.write( "f(x)= x^3-10x^2+34x+10
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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