Explained: "Determine which functions are polynomial functions. For those..."

College
Calculus and Analysis
Differential Calculus
Analyzing functions

kolonelyf4

Answered question

2021-11-23

Determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not.

G (x) = - 3 x^{2} {(x + 2)}^{3}

Answer & Explanation

kayleeveez7

Beginner2021-11-24Added 10 answers

Step1
We know,
A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer powers of variables.
Given,

f (x) = - 3 x^{2} {(x - 2)}^{3}

f (x) = - 3 x^{2} (x^{3} + 3 x^{2} (2) + 3 x {(2)}^{2} + 2^{3})

f (x) = - 3 x^{2} (x^{3} + 6 x^{2} + 12 x + 8)

f (x) = - 3 x^{5} - 18 x^{4} - 36 x^{3} - 24 x^{2}

Here, this is Sth degree of the polynomial. Step 2
Therefore,

f (x) = - 3 x^{5} - 18 x^{4} - 36 x^{3} - 24 x^{2}

is 5th degree of the polynomial.

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