SOLUTION: The graph of the polynomial function f(x)- Ax^3+Bx^2+Cx+D, where and A,B,C,and D are integers, has 3 x-intercepts at 1,2,and -6. If the graph passes thought the point M(3,18),

Question 102977: The graph of the polynomial function f(x)- Ax^3+Bx^2+Cx+D,
where and A,B,C,and D are integers, has 3 x-intercepts at 1,2,and -6.
If the graph passes thought the point M(3,18),
determine the values of A,B,C and D.
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
An x intercept is a where f(x)=0.
1.
2.
3.
and you know that
4.
Using the equations you get
1.

Four equations, four unknowns.
Since you didn't specify a method to choose, I'll choose a matrix method, if that's OK.
These equations can be represented as three matrices G, U, and V.

where [G]x[U]=[V]
Then [U]=[G]inv x [V]
Find the inverse of [G](using EXCEL) and multiply by [V]
The inverse of G is

Since [V] has all values of zero except the last value. The solution matrix,[U], is 18 multplied by the last column of the inverse matrix or

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