which of the functions,P,H,L,R, is a polynomial.The following are a number of terms. determine the coefficient and the degree of each a) (3/2)x to the power of five b) (root square of 2-root square of 5)x to the power nine c)7.3h to the power of to d) -13y to the power of seven e)(-5/7)x to the power of four
I'll do the first to get you started, you try the others and post back and someone will check your answers
a. 3/2 x^5
'x’ raised to the power ‘5’, this means the equation is a 5th degree equation.
the coefficient is number before the variable, in this case '3/2'
Now, you try the rest
To determine if a function is a polynomial, we need to check if it follows the definition of a polynomial function, which states that a polynomial is an algebraic expression with one or more terms, each consisting of a non-negative integer power of a variable multiplied by a coefficient.
Let's analyze each of the given functions:
a) (3/2)x^5
This function is a polynomial because it follows the definition. It has one term, which consists of the variable x raised to the 5th power.
b) (√2 - √5)x^9
This function is not a polynomial because it includes a square root. Polynomials only involve variables raised to non-negative integer powers and do not involve square roots or any other irrational functions.
c) 7.3h^2
This function is a polynomial because it follows the definition. It has one term, which consists of the variable h raised to the 2nd power.
d) -13y^7
This function is a polynomial because it follows the definition. It has one term, which consists of the variable y raised to the 7th power.
e) (-5/7)x^4
This function is a polynomial because it follows the definition. It has one term, which consists of the variable x raised to the 4th power.
To determine the coefficient and the degree of each term, we need to identify the coefficient and the highest power of the variable in each term.
a) Coefficient: 3/2, Degree: 5
b) Coefficient: (√2 - √5), Degree: 9 (However, this function is not a polynomial.)
c) Coefficient: 7.3, Degree: 2
d) Coefficient: -13, Degree: 7
e) Coefficient: -5/7, Degree: 4