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.

Roman Stevens

Expert

Step 1
Polynomials:
,${a}_{1}$${a}_{2}$...................${a}_{n}$ and  "n"  be  a  non-negatine   integer
A  polynomial  in  x  is  an  expression  of  the  form,

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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