document.write( "Question 825730: Write f(x)= x^3+9x^2+15x+58 in the form f(x)=(x-k)q(x)+r when k=-8. \n" ); document.write( "

Algebra.Com's Answer #497572 by jsmallt9(3758) $\"\"$ $\"About$

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If k = -8 then the desired form is:
\n" ); document.write( "f(x)=(x-(-8))q(x)+r
\n" ); document.write( "In order to rewrite f(x) in this form, we will use synthetic division to divide f(x) by (x-(-8)):
\n" ); document.write( "

\r\n" );
document.write( "-8  |  1   9   15   58\r\n" );
document.write( "-----     -8   -8  -56\r\n" );
document.write( "      -----------------\r\n" );
document.write( "       1   1    7    2\r\n" );
document.write( "

The 2 in the lower right corner is the remainder (the \"r\" in f(x)=(x-k)q(x)+r). The rest of the bottom row is the quotient (the q(x) in f(x)=(x-k)q(x)+r). The \"1 1 7\" translates into $\"x%5E2%2Bx%2B7\"$ . So the answer is:
\n" ); document.write( " $\"f%28x%29=%28x-%28-8%29%29%28x%5E2%2Bx%2B7%29%2B2\"$
\n" ); document.write( "or
\n" ); document.write( " $\"f%28x%29=%28x%2B8%29%28x%5E2%2Bx%2B7%29%2B2\"$

\n" ); document.write( "P.S. This is a polynomial, not a rational function. Please post in an appropriate category. \n" ); document.write( "

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