Questions: 2x^7+3x^6-12x^3+9 is Select an answer 2x^4+7/x^3-3x^2+12 is Select an answer 7x^3 is Select an answer 19x^6-8x^2+10 is Select an answer 5x^8+2 is Select an answer

2x^7+3x^6-12x^3+9 is Select an answer 2x^4+7/x^3-3x^2+12 is Select an answer 7x^3 is Select an answer 19x^6-8x^2+10 is Select an answer 5x^8+2 is Select an answer
Transcript text: $2 x^{7}+3 x^{6}-12 x^{3}+9$ is Select an answer $2 x^{4}+\frac{7}{x^{3}}-3 x^{2}+12$ is Select an answer $7 x^{3}$ is Select an answer $19 x^{6}-8 x^{2}+10$ is Select an answer $5 x^{8}+2$ is Select an answer
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Solution

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Determine whether \(2x^{7} + 3x^{6} - 12x^{3} + 9\) is a monomial, binomial, trinomial, other polynomial, or not a polynomial.

Step subtitle: Identify the number of terms

The expression \(2x^{7} + 3x^{6} - 12x^{3} + 9\) has four terms: \(2x^{7}\), \(3x^{6}\), \(-12x^{3}\), and \(9\).

Step subtitle: Classify the polynomial

Since the expression has four terms, it is classified as an "other polynomial."

\(\boxed{\text{Other polynomial}}\)

Determine whether \(2x^{4} + \frac{7}{x^{3}} - 3x^{2} + 12\) is a monomial, binomial, trinomial, other polynomial, or not a polynomial.

Step subtitle: Check for polynomial conditions

The term \(\frac{7}{x^{3}}\) can be rewritten as \(7x^{-3}\), which has a negative exponent. Polynomials cannot have negative exponents.

Step subtitle: Conclusion

Since the expression contains a term with a negative exponent, it is not a polynomial.

\(\boxed{\text{Not a polynomial}}\)

Determine whether \(7x^{3}\) is a monomial, binomial, trinomial, other polynomial, or not a polynomial.

Step subtitle: Identify the number of terms

The expression \(7x^{3}\) has only one term.

Step subtitle: Classify the polynomial

Since the expression has one term, it is classified as a "monomial."

\(\boxed{\text{Monomial}}\)

Determine whether \(19x^{6} - 8x^{2} + 10\) is a monomial, binomial, trinomial, other polynomial, or not a polynomial.

Step subtitle: Identify the number of terms

The expression \(19x^{6} - 8x^{2} + 10\) has three terms: \(19x^{6}\), \(-8x^{2}\), and \(10\).

Step subtitle: Classify the polynomial

Since the expression has three terms, it is classified as a "trinomial."

\(\boxed{\text{Trinomial}}\)

Determine whether \(5x^{8} + 2\) is a monomial, binomial, trinomial, other polynomial, or not a polynomial.

Step subtitle: Identify the number of terms

The expression \(5x^{8} + 2\) has two terms: \(5x^{8}\) and \(2\).

Step subtitle: Classify the polynomial

Since the expression has two terms, it is classified as a "binomial."

\(\boxed{\text{Binomial}}\)

\(\boxed{\text{Other polynomial}}\)
\(\boxed{\text{Not a polynomial}}\)
\(\boxed{\text{Monomial}}\)
\(\boxed{\text{Trinomial}}\)
\(\boxed{\text{Binomial}}\)

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