The polynomial $f(x)$ has degree 3. If $f(-1) = 15$, $f(0)= 0$, $f(1) = -5$, and $f(2) = 12$, then what are the $x$-intercepts of the graph of $f$?
+14903 The polynomial $f(x)$ has degree 3. If $f(-1) = 15$, $f(0)= 0$, $f(1) = -5$, and $f(2) = 12$, then what are the $x$-intercepts of the graph of $f$?
\(f(x)=y=ax^3+bx^2+cx+d\)
\(P_1(-1/15)\\P_2(0/0)\\P_3(1/-5)\\P_4(2/12)\)
\(y=ax^3+bx^2+cx+d\)
\(15=-a+b-c+d\)
\(0=d\)
\(-5=a+b+c +d\)
\(12=8a+4b+2c+d\)
a, b, c, d from the four linear equations comes slightly later.
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