document.write( "Question 1155338: Find the function f(x)=ax^3+bx^2+cx+d for which, f(-3)=-112, f(-1)=-2, f(1)=4, f(2)=13.\r
\n" ); document.write( "\n" ); document.write( "I know the answer is f(x) 3x^3-4x^2+5\r
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Algebra.Com's Answer #777924 by MathTherapy(10552) $\"\"$ $\"About$

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Find the function f(x)=ax^3+bx^2+cx+d for which, f(-3)=-112, f(-1)=-2, f(1)=4, f(2)=13.\r
\n" ); document.write( "\n" ); document.write( "I know the answer is f(x) 3x^3-4x^2+5\r
\n" ); document.write( "\n" ); document.write( "But, i would like to know how to solve this
\n" ); document.write( "

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document.write( "Given: f(- 3) = - 112, or (- 3, - 112)\r\n" );
document.write( "Substituting (- 3, - 112) in , we get:  ---- eq (i)\r\n" );
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document.write( "Given: f(- 1) = - 2, or (- 1, - 2)\r\n" );
document.write( "Substituting (- 1, - 2) in , we get:  ------ eq (ii)\r\n" );
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document.write( "Given: f(1) = 4, or (1, 4)\r\n" );
document.write( "Substituting (1, 4) in , we get:  ----------------- eq (iii)\r\n" );
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document.write( "Given:  f(2) = 13, or (2, 13)\r\n" );
document.write( "Substituting (2, 13) in , we get:  ---------------- eq (iv)\r\n" );
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document.write( "We now have:  \r\n" );
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document.write( "35A - 5B + 5C = 125____7A -  B + C = 25 ---- Subtracting eq (i) from eq (iv) -------- eq (v)\r\n" );
document.write( "                       7A + 3B + C = 9 ----- Subtracting eq (iii) from eq (iv) ------ eq (vi)\r\n" );
document.write( "                            4B = - 16 ------ Subtracting eq (v) from eq (vi)\r\n" );
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document.write( "        2B + 2D = 2____2(B + D) = 2(1) -- Adding eq (ii) & (iii) \r\n" );
document.write( "                         B + D = 1 ------ eq (vii)\r\n" );
document.write( "                       - 4 + D = 1 ------ Substituting - 4 for B in eq (vii)\r\n" );
document.write( "                            \r\n" );
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document.write( "A + B + C + D = 4\r\n" );
document.write( "A - 4 + C + 5 = 4 -------- Substituting - 4 for B, and 5 for D in eq (iii)\r\n" );
document.write( "                                      A + C = 3 ------ eq (viii)\r\n" );
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document.write( "8A + 4B + 2C + D = 13 ------- eq (iv)\r\n" );
document.write( "8A + 4(- 4) + 2C + 5 = 13 --- Substituting - 4 for B, and 5 for D in eq (iv)\r\n" );
document.write( "8A - 16 + 2C + 5 = 13\r\n" );
document.write( "8A + 2C = 24____2(4A + C) = 2(12)____4A + C = 12 ----- eq (ix)\r\n" );
document.write( "                                     3A = 9 ------ Subtracting eq (viii) from eq (ix)\r\n" );
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document.write( "                                  A + C = 3 ----- eq (viii)\r\n" );
document.write( "                                  3 + C = 3 ----- Substituting 3 for A in eq (viii)\r\n" );
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document.write( "With ,

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