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2021-02-03

Determine whether $g\left(x\right)=\frac{{x}^{3}}{2}-{x}^{2}+2$ is a polynomial. If it is, state its degree. If not, say why it is not a polynomial. If it is a polynomial, write it in standard form. Identify the leading term and the constant term.

Demi-Leigh Barrera

Skilled2021-02-04Added 97 answers

Step 1

Given:

$g\left(x\right)=\frac{{x}^{3}}{2}-{x}^{2}+2$

Step 2

Convert element to fracnion:$x}^{2}=\frac{{x}^{2}2}{2},2=\frac{2\times 2}{2$

$=\frac{{x}^{3}}{2}-\frac{{x}^{2}\times 2}{2}+\frac{2\times 2}{2}$

Since the denominators are equal, combine the fractions:$\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm b}{c}$

$=\frac{{x}^{3}-{x}^{2}\times 2+2\times 2}{2}$

Multiply the numbers:$2\times 2=4$

$g\left(x\right)=\frac{{x}^{3}-2{x}^{2}+4}{2}$

Hence, it is a polynomial with its degree 3,

Step 3

Now, convert 3 degree polynomial into standard form which is

$a{x}^{3}+b{x}^{3}+cx+d$

Standard form$\to g\left(x\right)=\frac{{x}^{3}}{2}-2{x}^{2}+0x+2$

Leading term$\to \frac{1}{2}$

Constant term$\to 2$

Given:

Step 2

Convert element to fracnion:

Since the denominators are equal, combine the fractions:

Multiply the numbers:

Hence, it is a polynomial with its degree 3,

Step 3

Now, convert 3 degree polynomial into standard form which is

Standard form

Leading term

Constant term

Jeffrey Jordon

Expert2022-07-06Added 2575 answers