joygielymmeloiy

2022-01-31

1. Is ${x}^{2}-2\sqrt{5}x+x$ a polynomial? If not, state a reason.

2. Is -2020x a polynomial? If not, state a reason.

3. Is$x\frac{2}{3}+3x+1$ a polynomial? If not, state a reason.

4. Is$\frac{1}{{x}^{2}}+\frac{r}{{x}^{3}}+\frac{r}{{x}^{4}}$ a polynomial? If not, state a reason.

5. Is$\pi$ a polynomial? If not, state a reason.

6. Is$x{3}^{\sqrt{2}}+checkmark3{x}^{2}$ a polynomial? If not, state a reason.

7. Is${x}^{3}+2x+1$ a polynomial? If not, state a reason.

8. Is$-2{x}^{-3}+{x}^{3}$ a polynomial? If not, state a reason.

9. Is$1-4{x}^{2}$ a polynomial? If not, state a reason.

2. Is -2020x a polynomial? If not, state a reason.

3. Is

4. Is

5. Is

6. Is

7. Is

8. Is

9. Is

Roman Stevens

Beginner2022-02-01Added 10 answers

Step 1

Polynomials:

$\text{Let}{a}_{0}$,${a}_{1}$, ${a}_{2}$...................${a}_{n}$ and "n" be a non-negatine integer

A polynomial in x is an expression of the form,

$\text{it}{a}_{n}{x}^{n}+{a}_{n-1}{x}^{n-1}+\dots \dots \dots \dots \dots \dots \dots \dots \dots +{a}_{1}x+{a}_{0}$

Step 2

A polynomial is a function with non-negative integral power.

Consider the polynomials,

${x}^{3}+2\sqrt{5x}+x$

It's not polynomials because polynomial have only integral power,

${x}^{3}+2\sqrt{5x}+x={x}^{3}+2{\left(5x\right)}^{\frac{1}{2}}+x$

It 's not a polynomials because term $2{\left(5x\right)}^{\frac{1}{2}}$ having fractional power.

Step 3

Consider the polynomials,

- 2020x

It is linear polynomials.

Therefore, -2020x is polynomials

Step 4

Consider the polynomials,

${x}^{\frac{2}{3}}+3x+1$

It is not a polynomial because the power of “x” $\left(\frac{2}{3}\right)$ having fractional power.

A polynomial only contains integer powers of "x."

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