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Let f, g, and h be polynomials such that \(h(x) = f(x)\cdot g(x)\). If the constant term of f(x) is -4 and the constant term of h(x) is 3, what is g(0)?

 Mar 19, 2020
 #1
avatar+485 
+1

Ok let's take a look at the first statement the problem gives us, which is that h(x) = f(x) * g(x). Since we know the constant terms of both of these terms, which are -4 and 3 respectively, that should hint at something already. Remember, the definition of the constant term is basically the term of an equation with no x coefficient(more or less). What that implies here is that these equations have some random preceding x terms, with the rightmost terms being -4 and 3 respectively. Remember, the question doesn't ask us to find these two equations explicitly. That's because we don't have to. It only asks us the value of g(0). Lucky for us, if f(x) = x^2 + x + 1, then when you have f(0), that causes all of the x's to become obsolete, leaving only the constant terms(remember plugging in the 0 for the x's?). That means since h(x) = f(x) * g(x), you can just ignore all the leading terms with x's, and rewrite it as: 3 = -4 * x  with x being the constant term of g(x). That gives us the constant term of g(x) which is -3/4

 Mar 20, 2020
 #2
avatar+724 
0

Thank you!

 Mar 20, 2020
 #3
avatar+485 
+1

No problem!

jfan17  Mar 21, 2020

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