Question

1) Classify the following polynomial by degree. p(p - 5) + 6

Answer 1

Answer:

1. D quadratic

2.  D monomial

3.  B) Monomial

4. C) Constant

Step-by-step explanation:

1) Classify the following polynomial by degree. p(p - 5) + 6

p(p - 5) + 6

Distribute

p^2 -5p +6

This has 3 terms so it is a trinomial and is of the second order so it is quadratic.  We are to classify it by degree (order) so it is quadratic

A) Binomial

B) Trinomial  

C) Linear

D) Quadratic*****

2) Classify the following polynomial by number of terms. 5m^2 - 3m^2

5m^2 - 3m^2

2m^2

The polynomial as written has 2 terms, but can be simplified to one term.  I always had students simplify first before classifying

I would call it monomial.  Check your notes if your instructor does it differently.

A) Linear

B) Binomial  

C) Quadratic

D) Monomial

3) Classify the following polynomial by number of terms. 2 + 3x^3 - 2

2 + 3x^3 - 2

Again, I teach simplify first

2-2 goes away

3x^3  

This has 1 term so it is a monomial

A) Binomial

B) Monomial

C) Constant  

D) Cubic

4) Classify the following polynomial by degree. -3 + 3x - 3x

-3 + 3x - 3x

Again I teach simplify first, so 3x-3x goes away

-3

This is a constant term

A) Trinomial

B) Linear

C) Constant

D) Monomial

Answer 2

1). p(p - 5) + 6

Distributive property.

p^2 - 5p + 6

This is a trinomial of degree two because of the fact that it contains three terms, and it's highest degree is two.

2).

5m^2 - 3m^2

Combine like terms.

2m^2

This is a monomial because it contains one term.

3). 2 + 3x^3 - 2

Combine like terms.

3x^3

This is a monomial because it contains one term.

4). -3 + 3x - 3x

Combine like terms.

-3

This is a constant, as there are no variables, and only one term.