document.write( "Question 947462: P(x) = 4x^4 + 30x^3 − 40x^2 + 36x + 11, c = −5. How to solve with synthetic division and the Remainder Theorem? \n" ); document.write( "

Algebra.Com's Answer #578147 by josgarithmetic(39618) $\"\"$ $\"About$

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Maybe you want to check if the root or binomial (x+c) is one of the factors of P(x). If remainder from synthetic division is 0 then Factor Theorem tells you that x+c is one of the factors of P. If the remainder from synthetic division is not zero, then the Remainder theorem tells you that P(c)=theRemainder, or in your example, P(-5)=theRemainder.\r
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\n" ); document.write( "\n" ); document.write( "_______________|__________
\n" ); document.write( "_______________|________________________________________________
\n" ); document.write( "_______________|________4_____30______-40_______36_______11
\n" ); document.write( "________-5_____|
\n" ); document.write( "_______________|_____________-20______-50______450______-2430
\n" ); document.write( "_______________|____________________________________________________
\n" ); document.write( "________________________4_____10______-90_______486______-2419\r
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\n" ); document.write( "\n" ); document.write( "-5 is NOT a root of P.
\n" ); document.write( "P(-5)=-2419. \n" ); document.write( "

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