src/Advanced/Tropical Polynomials/parts/00 arithmetic.typ

@@ -104,7 +104,7 @@ Is there a tropical multiplicative identity? \
 Do tropical multiplicative inverses always exist? \
 #note([
   For every $x != #sym.infinity$, does there exist an inverse $y$ so that $x #tm y = i$, \
-  where $i$ is the additive identity?
+  where $i$ is the multiplicative identity?
 ])
 
 #solution([Yes, it is $-x$. For $x != 0$, $x #tm (-x) = 0$])

src/Advanced/Tropical Polynomials/parts/02 cubic.typ

@@ -5,7 +5,7 @@
 = Tropical Cubic Polynomials
 
 #problem()
-Consider the polynomial $f(x) = x^3 #tp x^2 #tp 3x #tp 6$. \
+Consider the polynomial $f(x) = x^3 #tp 1x^2 #tp 3x #tp 6$. \
 - sketch a graph of this polynomial
 - use this graph to find the roots of $f$
 - write (and expand) a product of linear factors with the same graph as $f$.
@@ -43,7 +43,7 @@ Consider the polynomial $f(x) = x^3 #tp x^2 #tp 3x #tp 6$. \
 #pagebreak() // MARK: page
 
 #problem()
-Consider the polynomial $f(x) = x^3 #tp x^2 #tp 6x #tp 6$. \
+Consider the polynomial $f(x) = x^3 #tp 1x^2 #tp 6x #tp 6$. \
 - sketch a graph of this polynomial
 - use this graph to find the roots of $f$
 - write (and expand) a product of linear factors with the same graph as $f$.
@@ -118,10 +118,10 @@ Using the last three problems, find formulas for $B$ and $C$ in terms of $a$, $b
 #solution([
 
   $
-    B = min(b, (a+c)/2, (2a+d)/2)
+    B = min(b, (a+c)/2, (2a+d)/3)
   $
   $
-    C = min(c, (b+d)/2, (a+2d)/2)
+    C = min(c, (b+d)/2, (a+2d)/3)
   $
 ])