document.write( "Question 1099067: Find a polynomial with integer coefficients that satisfies the given conditions.
\n" ); document.write( "Q has degree 3 and zeros −4 and 1 + i\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "I do not know how to do this could you please help me.
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #713467 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\r\n" );
document.write( "Since 1 + i is a solution, so is its conjugate 1 - i\r\n" );
document.write( "\r\n" );
document.write( "Set x = to each and get 0 on the right of each equation:\r\n" );
document.write( "\r\n" );
document.write( "  x = -4;       x = 1+i;         x = 1-i\r\n" );
document.write( "x+4 = 0;    x-1-i = 0;       x-1+i = 0\r\n" );
document.write( "\r\n" );
document.write( "Multiply left sides and right sides of the three equations:\r\n" );
document.write( "\r\n" );
document.write( "      (x+4)(x-1-i)(x-1+i) = (0)(0)(0)\r\n" );
document.write( "\r\n" );
document.write( "Multiply and simplify:\r\n" );
document.write( "\r\n" );
document.write( "  (x+4)[(x-1)-i][(x-1)+i] = 0  \r\n" );
document.write( "\r\n" );
document.write( "         (x+4)[(x-1)²-i²] = 0\r\n" );
document.write( "\r\n" );
document.write( "Square the binomial and replace i² by -1\r\n" );
document.write( "\r\n" );
document.write( "      (x+4)[x²-2x+1-(-1)] = 0\r\n" );
document.write( "\r\n" );
document.write( "         (x+4)[x²-2x+1+1] = 0\r\n" );
document.write( "\r\n" );
document.write( "           (x+4)[x²-2x+2] = 0 \r\n" );
document.write( "\r\n" );
document.write( "       x³-2x²+2x+4x²-8x+8 = 0\r\n" );
document.write( "\r\n" );
document.write( "              x³+2x²-6x+8 = 0   \r\n" );
document.write( "\r\n" );
document.write( "So the polynomial Q(x) is\r\n" );
document.write( "\r\n" );
document.write( "                     Q(x) = x³+2x²-6x+8    \r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );