Question

basic polynomial operations
date__________ period
name each polynomial by degree and number of terms.

1. $-10x$
2. $-10r^4 - 8r^2$
3. $7$
4. $9a^6 + 3a^5 - 4a^4 - 3a^2 + 9$
5. $-3n^3 + n^2 - 10n + 9$
6. $7x^2 - 9x - 10$
7. $-4b$
8. $-9 + 7n^3 - n^2$

Explanation:

Step1: Identify degree & term count for 1)

Degree: highest exponent ($x^1$) = 1; Terms: 1. Name: Linear monomial.

Step2: Identify degree & term count for 2)

Degree: highest exponent ($r^4$) = 4; Terms: 2. Name: Quartic binomial.

Step3: Identify degree & term count for 3)

Degree: constant term = 0; Terms: 1. Name: Constant monomial.

Step4: Identify degree & term count for 4)

Degree: highest exponent ($a^6$) = 6; Terms: 5. Name: Sixth-degree polynomial.

Step5: Identify degree & term count for 5)

Degree: highest exponent ($n^3$) = 3; Terms: 4. Name: Cubic polynomial.

Step6: Identify degree & term count for 6)

Degree: highest exponent ($x^2$) = 2; Terms: 3. Name: Quadratic trinomial.

Step7: Identify degree & term count for 7)

Degree: highest exponent ($b^1$) = 1; Terms: 1. Name: Linear monomial.

Step8: Identify degree & term count for 8)

Degree: highest exponent ($n^3$) = 3; Terms: 3. Name: Cubic trinomial.

Answer:

1. Linear monomial
2. Quartic binomial
3. Constant monomial
4. Sixth-degree polynomial
5. Cubic polynomial
6. Quadratic trinomial
7. Linear monomial
8. Cubic trinomial