document.write( "Question 125808This question is from textbook Introductory Algebra
\n" ); document.write( ": If anyone could help me with this problem, it would be greatly appreciated. The problem reads: A polynomial in x has degree 3. The coefficient of x^2 is 3 less than the coefficient of x^3. The coefficient of x is three times the coefficient of x^2. The remaining coefficient is 2 more than the coefficient of x^3. The sum of the coefficient is -4. Find the polynomial. \n" ); document.write( "

Algebra.Com's Answer #92192 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "A polynomial of degree $\"3\"$ : $\"ax%5E3+%2B+b+x%5E2+%2B+cx+%2B+d=0\"$ \r
\n" ); document.write( "\n" ); document.write( "The coefficient of x^2 ( $\"b\"$ ) is 3 less than the coefficient of x^3 ( $\"a\"$ )\r
\n" ); document.write( "\n" ); document.write( " $\"a+=+b+%2B+3\"$ \r
\n" ); document.write( "\n" ); document.write( "The coefficient of x ( $\"c\"$ ) is three times the coefficient of x^2 ( $\"b\"$ )\r
\n" ); document.write( "\n" ); document.write( " $\"c+=+3b+\"$
\n" ); document.write( "
\n" ); document.write( "The remaining coefficient ( $\"d\"$ ) is 2 more than the coefficient of x^3 ( $\"a\"$ ) .\r
\n" ); document.write( "\n" ); document.write( " $\"d+=+a+%2B+2+\"$
\n" ); document.write( " \r
\n" ); document.write( "\n" ); document.write( "The sum of the coefficients is -4.\r
\n" ); document.write( "\n" ); document.write( " $\"a%2Bb%2Bc%2Bd=-4+\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( " $\"c+=+3b+\"$ ЕЕЕЕЕЕ.(2)
\n" ); document.write( " $\"d+=+a+%2B+2+\"$ ЕЕЕЕЕ..(3)
\n" ); document.write( " $\"a%2Bb%2Bc%2Bd=-4+\"$ ЕЕЕЕ(4)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"a+=+b+%2B+3\"$ ЕЕЕЕЕ(1)..=>Е.plug in (3)
\n" ); document.write( " $\"d+=+a+%2B+2+\"$ ЕЕЕЕЕ..(3)
\n" ); document.write( " $\"d+=+b+%2B+3+%2B+2+\"$ Е
\n" ); document.write( " $\"d+=+b+%2B+5+\"$ ЕЕЕЕЕЕЕ.(I)\r
\n" ); document.write( "\n" ); document.write( " $\"a%2Bb%2Bc%2Bd=-4+\"$ ЕЕЕЕ(4).substitute $\"a\"$ from (1), $\"c\"$ from (3), and $\"d\"$ from (I)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%28+b+%2B+3%29+%2B+b+%2B+3b++%2B+%28b+%2B+5+%29+=+-4+\"$ ЕЕsolve for $\"b\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"6+b+%2B+8+=+-4+\"$ ЕЕ\r
\n" ); document.write( "\n" ); document.write( " $\"6+b+=+-4-8+\"$ ЕЕ\r
\n" ); document.write( "\n" ); document.write( " $\"6+b+=+-12+\"$ ЕЕ\r
\n" ); document.write( "\n" ); document.write( " $\"b+=+-2+\"$ ЕЕ\r
\n" ); document.write( "\n" ); document.write( "Now find $\"a\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"a+=+b+%2B+3\"$ ЕЕЕЕЕ(1)\r
\n" ); document.write( "\n" ); document.write( " $\"a+=+-2+%2B+3\"$
\n" ); document.write( " $\"a+=+1\"$ \r
\n" ); document.write( "\n" ); document.write( "Now find $\"c\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"c+=+3b+\"$ ЕЕЕЕЕЕ.(2)
\n" ); document.write( " $\"c+=+3%28-2%29+\"$
\n" ); document.write( " $\"c+=+-6+\"$ \r
\n" ); document.write( "\n" ); document.write( "Now find $\"d\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"d+=+b+%2B+5+\"$ ЕЕЕЕЕЕЕ.(I)
\n" ); document.write( " $\"d+=+-2+%2B+5+\"$ ЕЕ
\n" ); document.write( " $\"d+=+3+\"$ ЕЕ\r
\n" ); document.write( "\n" ); document.write( "So, your coefficients are:\r
\n" ); document.write( "\n" ); document.write( " $\"a+=+1\"$
\n" ); document.write( " $\"b+=+-2+\"$ ЕЕ
\n" ); document.write( " $\"c+=+-6+\"$
\n" ); document.write( " $\"d+=+3+\"$ ЕЕ\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "A polynomial of degree $\"3\"$ will be: $\"x%5E3+-2x%5E2+-6x+%2B+3+=+0\"$ \r
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