Question 1063845
<pre>
{{{Polynomial=Ax^3+Bx^2+Cx+D="P(x)"}}}

Substitute given points:

{{{system(
matrix(4,9,

(-2)^3A,""+"", (-2)^2B,""+"", (-2)C,""+"", D, ""="", 29,
(-1)^3A,""+"", (-1)^2B,""+"", (-1)C,""+"", D, ""="", 12,
( 1)^3A,""+"",  (1)^2B,""+"",  (1)C,""+"", D, ""="", -2,
 (3)^3A,""+"",  (3)^2B,""+"",  (3)C,""+"", D, ""="", 56))

}}}

Write the matrix for the system

{{{(matrix(4,6,

(-2)^3, (-2)^2, (-2), 1, "|", 29,
(-1)^3, (-1)^2, (-1), 1, "|", 12,
( 1)^3,  (1)^2,  (1), 1, "|", -2,
 (3)^3,  (3)^2,  (3), 1, "|", 56)))}}}

In row-reduced echelon form is:

{{{(matrix(4,9,
1,"",0,"",0,"",0,"|",17/15,
0,"",1,"",0,"",0,"|",28/5,
0,"",0,"",1,"",0,"|",-122/15,
0,"",0,"",0,"",1,"|",-3/5


)))}}}

So polynomial is

{{{expr(17/15)x^3+expr(28/5)x^2-expr(122/15)x-3/5}}}

Edwin</pre>