document.write( "Question 141373This question is from textbook Introductory Algebra
\n" ); document.write( ": I was hoping you could provide me some direction as to how to solve this polynomial word problem.\r
\n" ); document.write( "\n" ); document.write( "A polynomial in x has degree 3. The coefficient of x(with an exponent of 2) is 3 less than the coefficient of x(with an exponent of 3). The coefficient of x is three times the coefficient of x(with an exponent of 2). The remaining coefficient is 2 more than the coefficient of x(with an exponent of 3). The sum of the coefficients is -4. Find the polynomial. \n" ); document.write( "
Algebra.Com's Answer #103014 by ankor@dixie-net.com(22740)\"\" \"About 
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A polynomial in x has degree 3. The coefficient of x(with an exponent of 2) is 3 less than the coefficient of x(with an exponent of 3). The coefficient of x is three times the coefficient of x(with an exponent of 2). The remaining coefficient is 2 more than the coefficient of x(with an exponent of 3). The sum of the coefficients is -4. Find the polynomial.
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\n" ); document.write( "Let a = coefficient of x^3
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\n" ); document.write( "Write an expression for each statement:
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\n" ); document.write( "\"The coefficient of x^2 is 3 less than the coefficient of x^3\"
\n" ); document.write( "(a-3)
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\n" ); document.write( "\"The coefficient of x is three times the coefficient of x^2.\"
\n" ); document.write( "3(a-3)
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\n" ); document.write( "\"The remaining coefficient is 2 more than the coefficient of x^3\".
\n" ); document.write( "(a+2)
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\n" ); document.write( "\"The sum of the coefficients is -4.\"
\n" ); document.write( "a + (a-3) + 3(a-3) + (a+2) = -4
\n" ); document.write( "a + a - 3 + 3a - 9 + a + 2 = -4
\n" ); document.write( "6a - 10 = -4
\n" ); document.write( "6a = -4 + 10
\n" ); document.write( "6a = +6
\n" ); document.write( "a = +1
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\n" ); document.write( "Using a = 1 we can write it:
\n" ); document.write( "(1)x^3 + (1-3)x^2 + 3(-2)x + (1+2)
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\n" ); document.write( "y = x^3 - 2x^2 - 6x + 3; is the polynomial
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\n" ); document.write( "Did this help?\r
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