document.write( "Question 366515: Given f(x)=x^3+6x^2+11x+6 Show that f(-2)=0 and find the three factors of f(x) \n" ); document.write( "
Algebra.Com's Answer #261181 by CharlesG2(834)\"\" \"About 
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Given f(x)=x^3+6x^2+11x+6 Show that f(-2)=0 and find the three factors of f(x)\r
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\n" ); document.write( "\n" ); document.write( "f(x)=x^3+6x^2+11x+6
\n" ); document.write( "f(-2) = (-2)^3 + 6(-2)^2 + 11(-2) + 6
\n" ); document.write( "f(-2) = -8 + 6 * 4 - 22 + 6
\n" ); document.write( "f(-2) = -8 + 24 - 22 + 6
\n" ); document.write( "f(-2) = 16 - 22 + 6
\n" ); document.write( "f(-2) = -6 + 6
\n" ); document.write( "f(-2) = 0, so x = -2 is a root when f(x) = 0, so that means x + 2 is a factor\r
\n" ); document.write( "\n" ); document.write( "..........x^2 + 4x + 3
\n" ); document.write( "x + 2 --> x^3 + 6x^2 + 11x + 6
\n" ); document.write( "..........x^3 + 2x^2
\n" ); document.write( "................4x^2 + 11x
\n" ); document.write( "................4x^2 + 8x
\n" ); document.write( "........................3x + 6
\n" ); document.write( "........................3x + 6\r
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\n" ); document.write( "\n" ); document.write( "x^2 + 4x + 3
\n" ); document.write( "(x + 1)(x + 3) --> test with FOIL, First Outer Inner Last
\n" ); document.write( "x^2 + 3x + x + 3
\n" ); document.write( "x^2 + 4x + 3, yes\r
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\n" ); document.write( "\n" ); document.write( "the factors are x + 2, x + 1, x + 3
\n" ); document.write( "the roots are -2, -1, -3\r
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