document.write( "Question 239325: for problem use the Remaider Theorem to find P(c)\r
\n" ); document.write( "\n" ); document.write( "P(x)=5x^3-4x^2+x-7, c=3 \n" ); document.write( "

Algebra.Com's Answer #175733 by jsmallt9(3758) $\"\"$ $\"About$

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The Remainder Theorem tells us that if some polynomial P(x) is divided by (x-c) then
\n" ); document.write( "P(x) = Q(x)(x-c) + R
\n" ); document.write( "where Q(x) is the quotient and R is the remainder of the division. Then
\n" ); document.write( "P(c) = Q(c)((c)-c) + R
\n" ); document.write( "Since (c-c) = 0 it will not matter what Q(c) is because when you multiply whatever Q(c) is by 0 you will get 0. And since 0+R = R, P(c) = R.

\n" ); document.write( "So we can find P(c) by using the remainder of dividing P(x) by (x-c). In your problem c = 3 so we will divide by (x-3) (using Synthetic Division):
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document.write( "3 |   5   -4   1   -7\r\n" );
document.write( "---       15  33  102\r\n" );
document.write( "     ----------------\r\n" );
document.write( "      5   11  34   95\r\n" );
document.write( "

\n" ); document.write( "So P(3) = 95.

\n" ); document.write( "(You should get the same answer if you use Long Division instead of Synthetic Division.) \n" ); document.write( "

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