document.write( "Question 1169758: given the polynomial P(x)=x^4-2x^3-7x^2+18x-18
\n" ); document.write( "a. without long division, find the remainder if P is divided by x+1
\n" ); document.write( "b. if one zero of P is 1-i, find the remaining zeros of P
\n" ); document.write( "c. write P in factored form \n" ); document.write( "

Algebra.Com's Answer #794576 by math_helper(2461) $\"\"$ $\"About$

You can put this solution on YOUR website!


\n" );
document.write( "a) Use synthetic division:
\n" );
document.write( "For the divisor, the form is x-a, so for x+1 we have a=-1:\r
\n" );
document.write( "\n" );
document.write( " -1 | 1  -2  -7  18  -18
\n" );
document.write( "    |    -1   3   4  -22
\n" );
document.write( "    |____________________
\n" );
document.write( "      1  -3  -4  22  -40    --> Remainder is -40\r
\n" );
document.write( "\n" );
document.write( "b) If  x=1-i  is a root, then too must be x=1+i as complex roots always come in conjugate pairs.    ... and now we can divide:\r
\n" );
document.write( "\n" );
document.write( "     --> x=-3 and x=3 are also zeros\r
\n" );
document.write( "\n" );
document.write( "c)  Part (b) has the four factors, using real valued polynomials: 
\n" );
document.write( "  \r
\n" );
document.write( "\n" );
document.write( "  \n" );
document.write( "

\n" );