document.write( "Question 710827: Hi, I am working on finding the zeros of a polynomial function and don't understand it. I also don't have access to a calculator right now. I need help on this problem: f(x) = x^4 + x^3 + 2x^2 + 4x - 8. To find all zeros of the polynomial function, I know that I would have to use synthetic division but where do I start? Thanks! \n" ); document.write( "
Algebra.Com's Answer #437225 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
f(x) = x^4 + x^3 + 2x^2 + 4x - 8. To find all zeros of the polynomial function,
\n" ); document.write( "Use the factors of -8, to perform synthetic division, how about x=-2
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\n" ); document.write( ". . .__________________
\n" ); document.write( "-2 | 1 + 1 + 2 + 4 - 8
\n" ); document.write( ".. . . . . -2 + 2 - 8 + 8
\n" ); document.write( ". . -------------------
\n" ); document.write( ". . . 1 - 1 + 4 - 4 + 0
\n" ); document.write( ":
\n" ); document.write( "we now have (x + 2)(x^3 - x^2 + 4x - 4)
\n" ); document.write( "we could us synthetic division again but this will group factor
\n" ); document.write( "(x^3 - x^2) + (4x - 4)
\n" ); document.write( "x^2(x - 1) + 4(x - 1)
\n" ); document.write( "Factor out (x-1)
\n" ); document.write( "(x - 1)(x^2 + 4)
\n" ); document.write( "now we have
\n" ); document.write( "(x + 2)(x - 1)(x^2 + 4)
\n" ); document.write( "only two real solutions
\n" ); document.write( "x = -2
\n" ); document.write( "x = +1
\n" ); document.write( ":
\n" ); document.write( "I did confirm this on my calculator
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