What is the degree of the following monomial?

Question

1. What is the degree of the following monomial?
-3f^3g^4h^5


2. Which of the following expressions is a polynomial?
F(x)=-3x^4√x+13x^2-5x
F(x)=2/x^2-15x
F(x)=x^3-11x^2+3^x
F(x)=2x^3-5x^5-2/9x^2+9

3. What is another name for this polynomial, based on the number of terms it contains?
G(x)=5x^9+17x^5

4. Based on its degree, what kind of polynomial is this?
H(x)=4x^4+2x-5

5. For the polynomial shown below, find f(-1).
F(x)=3x^4-x^3+4x-2

 

17.Identify the relative minimum value for the function shown below.
G(x)=x^3-3x^2+2

Answer 1

17 The relative minimum (or turning point) value of G(x)=x^3-3x^2+2 is the point at which the slop of the curve is zero and that the graph is concave up around that point. If you draw the graph (or just take the derivative) you will see that the graph turns twice (at (0,2) and (2,-10)). This means the relative minimum occurs at x=2 and it is equal to y=-10.

 

15 F(-1)=3(-1)⁴-(-1)³+4(-1)-2 = 3--1-4-2 = -2

 

4 Based on its degree H(x)=4x^4+2x-5  is a forth degree polynomial.

 

3 Another name for this polynomial G(x)=5x^9+17x^5, based on the number of terms it contains, is trinomial.

 

2 None of them are polynomial.

F(x)=-3x^4√x+13x^2-5x because of a none-positive integer power X^½
F(x)=2/x^2-15x because, again none-positive power
F(x)=x^3-11x^2+3^x because the term 3^x is exponential and not polynomial by definition
F(x)=2x^3-5x^5-2/9x^2+9 because it is polynomial over polynomial (rational) by defination

 

1 No degree can be spoken of for -3f^3g^4h^5  because which is the variable and which is constant is not defined. If any more than one of them is variable, then the function is not polynomial and we can't speak of degree.