document.write( "Question 848809: If someone could please help me with this, it will be greatly appreciated!\r
\n" ); document.write( "\n" ); document.write( "If x + 1 is a factor of ax^4 + bx^2 + c, what is the value of a + b + c?
\n" ); document.write( "My work so far before getting stuck:\r
\n" ); document.write( "\n" ); document.write( "I was trying to use Synthetic division, but evidently it didn't work out as I had hoped:\r
\n" ); document.write( "\n" ); document.write( "-1 ˩.a..b..І..c
\n" ); document.write( ".......Ab..І.ab-b
\n" ); document.write( ".....a.ab-bІ.1 \r
\n" ); document.write( "\n" ); document.write( "1=c-ab-b
\n" ); document.write( " \r
\n" ); document.write( "\n" ); document.write( "1=c-ab-b
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #511283 by fcabanski(1391) $\"\"$ $\"About$

You can put this solution on YOUR website!
When you perform the synthetic division, remember the coefficients of x^3 and x. Both are 0. That will lead to the correct answer. The final factor has to be = to 0. It will be a+b+c.

\n" ); document.write( "The other way to solve this is:

\n" ); document.write( "If x+1 is a factor of the polynomial p(x), x=-1 and p(-1) = 0 according to the remainder theorem.

\n" ); document.write( "Set p(-1) = 0. Then solve for a+b+c

\n" ); document.write( " $\"ax%5E4+%2B+bx%5E2+%2B+c+=+0\"$
\n" ); document.write( "

$\"+a%28-1%29%5E4+%2B+b%28-1%29%5E2+%2B+c+=+0\"$

\n" ); document.write( "a+b+c = 0
\n" ); document.write( " \n" ); document.write( "

\n" );