document.write( "Question 1155595: Let $\"+h%28x%29=4x%5E2%2B15x%5E3-10x%2B2+\"$ . Express h(x) in the form h(x)=q(x)(x+3)+r where q(x) is a polynomial and r is a number. Use the Remainder Theorem to check that you have the correct remainder. \n" ); document.write( "

Algebra.Com's Answer #778190 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " $\"+h%28x%29=4x%5E2%2B15x%5E3-10x%2B2+\"$ ....rearrange terms
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\n" ); document.write( " $\"+h%28x%29=15x%5E3%2B4x%5E2-10x%2B2+\"$ \r
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\n" ); document.write( "\n" ); document.write( "Express $\"h%28x%29\"$ in the form $\"h%28x%29=q%28x%29%28x%2B3%29%2Br+\"$ where $\"q%28x%29\"$ is a polynomial and $\"r\"$ is a number. \r
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\n" ); document.write( "\n" ); document.write( "...........( $\"15x%5E2-41x%2B113\"$
\n" ); document.write( " $\"%28x%2B3%29\"$ | $\"15x%5E3%2B4x%5E2-10x%2B2+\"$
\n" ); document.write( "........... $\"15x%5E3%2B45x%5E2\"$
\n" ); document.write( "................ $\"-41x%5E2-10x\"$
\n" ); document.write( "................ $\"-41x%5E2-123x\"$
\n" ); document.write( "....................... $\"113x%2B2\"$
\n" ); document.write( "....................... $\"113x%2B339\"$
\n" ); document.write( "........................... $\"-337\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"q%28x%29=15x%5E2-41x%2B113\"$ is a polynomial and $\"r=-337\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"h%28x%29=%2815x%5E2-41x%2B113%29%28x%2B3%29-337+\"$ \r
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