Question
Determine if the function reprsents a polynomial, and for those that are state their degree. 13) -2a^5+10a^6 14) 4x^6 15) x^4cdot (x-1)^2cdot (x+2.5)^3 16) sqrt (x)+1 17) (x^2+2)/(3) 18) x^(1)/(3)+7x^2-2 19) (x+2)^3cdot (x-(3)/(5))^2 20) 3x^2+7x-(2)/(3x) 21) (x-(1)/(4))^4cdot (x+sqrt (7))^2 22) (x+1)/(x^2)
Solution
4.3
(311 Votes)
Jazmin
Professional ยท Tutor for 6 years
Answer
### 13) Degree 6### 14) Degree 6### 15) Degree 9### 16) Not a polynomial### 17) Degree 2### 18) Not a polynomial### 19) Degree 5### 20) Not a polynomial### 21) Degree 6### 22) Not a polynomial
Explanation
## Step 1: Analyzing the terms of each expression### We examine each term of the given expressions to determine if they fit the definition of a polynomial. A polynomial has only non-negative integer exponents on its variables.## Step 2: Identifying Polynomials and their Degrees### For expressions that are polynomials, we identify the highest power of the variable, which represents the degree of the polynomial.## Step 3: Results for each expression### 13)
: This is a polynomial. The highest power is 6, so the degree is 6.### 14)
: This is a polynomial. The highest power is 6, so the degree is 6.### 15)
: This is a polynomial. Expanding the expression would result in a highest power of
, so the degree is 9.### 16)
: This is not a polynomial because
and
is not an integer.### 17)
: This is a polynomial. It can be rewritten as
. The highest power is 2, so the degree is 2.### 18)
: This is not a polynomial because
has a non-integer exponent.### 19)
: This is a polynomial. Expanding the expression would result in a highest power of
, so the degree is 5.### 20)
: This is not a polynomial because
and -1 is a negative exponent.### 21)
: This is a polynomial. Expanding the expression would result in a highest power of
, so the degree is 6.### 22)
: This is not a polynomial because
, which contains negative exponents.