How do you write a polynomial in standard form, then classify it by degree and number of terms #-4p+3p+2p^2#?

Question

How do you write a polynomial in standard form, then classify it by degree and number of terms  #-4p+3p+2p^2#?

Eli Assouline · Accepted Answer

Standard form : #2p^2-p#
Classify by degree: Quadratic
Classify by number of terms: Binomial

Standard form suggests that
- Combine all like terms together
- Rearrange it so that the degrees are arranged in a descending order from left to right.

So in #-4p+3p+2p^2#

We first combine like terms together

#-p+2p^2#

#Note: -4+3=-1, -1p=-p#

Now we rearrange it so the degrees are in descending order

#2p^2-p#

We can see that the degree in #p^2# is two, so it is classified as a quadratic.

We can also see that there are two terms in this equation, so it is classified as a binomial.
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Extra examples:

Genesis Allen · Answer

undefined The polynomial written in standard form is $ 2p^2 - p $. 
It is classified as:
- Degree: 2 (quadratic)
- Number of terms: 2

Nathan Axel · Answer

undefined To write the polynomial in standard form, combine like terms to simplify it.

-4p + 3p + 2p^2 = (2p^2) + (-4p + 3p) = 2p^2 - p

The polynomial in standard form is 2p^2 - p.

Now, to classify it:
- The degree of the polynomial is the highest power of the variable, which is 2. So, it's a quadratic polynomial.
- The number of terms in the polynomial is the count of distinct monomials separated by addition or subtraction signs, which is 2. So, it's a binomial polynomial.