SOLUTION: given f(x)=x^3-2x+1 and g(x)=-x^2-5x+12 find (f+g)(x)

Question 1201268: given f(x)=x^3-2x+1 and g(x)=-x^2-5x+12 find (f+g)(x)
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.

(f+g)(x) = x^3 - x^2 - 7x + 13.

It is the same as to combine like terms when you add expressions.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
(f+g)(x) is equal to f(x) + g(x)
f(x) = x^3 - 2x + 1
g(x) = -x^2 - 5x + 12
f(x) + g(x) = x^3 - x^2 - 7x + 13
when x = 3, you get:
f(x) = 3^3 - 2*3 + 1 = 27 - 6 + 1 = 22
g(x) = -3^2 - 5*3 + 12 = -9 - 15 + 12 = -12
f(x) + g(x) = 22 - 12 = 10
(f+g)(x) = f(x) + g(x) = x^3 - x^2 - 7x + 13
when x = 3, this becomes (f+g)(x) = 3^3 - 3^2 - 7*3 + 13 = 27 - 9 - 21 + 13 = 27 + 13 - 9 - 21 = 40 - 30 = 10
since 22 - 12 = 10, that checks out ok.
the rule is:
(f+g)(x) is equal to f(x) + g(x)
when you add f(x) to g(x), you combine like terms and keep the unlike terms separate.
the unlike terms were the x^3 term the x^2 term.
the like terms were the x terms and the constant terms.
x^3 and x^2 were kept separate.
-5x and -2x were added together.
+1 and +12 were also added together.
the result was x^3 - x^2 - 7x + 13

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