Polynomial Vocabulary
What is a variable?
An unknown value represented with a letter or symbol.
Simplify 3x+4x
7x
What is the degree of polynomial is x2+5x+6?
quadratic or 2
What are the 2 steps to adding polynomials?
1. Combine like terms
2. Make sure it's in standard form
What are the 3 steps to subtracting polynomials?
1. Distribute the negative to everything behind it.
2. Combine like terms
3. Make sure it's in standard form
(Keep, Change, Change)
Define the term "leading coefficient."
The coefficient of the term with the highest degree.
What do you get when you combine 5a2+2a−3a2+4?
2a2 + 2a + 4
Is 2y2+3y+7 a monomial, binomial, or trinomial?
trinomial
Solve: (3x2+5x) + (2x2+4)
5x2 +5x + 4
What is (5x2+3x)−(2x2+x)?
3x2 + 2x
What does it mean for a polynomial to be in standard form?
When terms are arranged in descending order of the exponents of the variable.
Combine 7m+2m2+3m−m2. (make sure your answer is in standard form!)
m2 + 10m
True or False: x2+5x+6, is a quartic trinomial.
False, it is a quadratic trinomial.
Add the polynomials (2x3+3x2−x) and (x3−2x2+5).
3x3 + x2 - x + 5
What is the result of (6x3+4x2−x)−(2x3−3x+5)?
4x3 + 4x2 - 2x + 5
What is a constant term in a polynomial?
The term that does not contain any variable
Simplify 9x3+3x2−4x3+2x.
5x3 + 3x2 +2x
Classify 4x3−2x+1.
cubic trinomial
If you add 3x2+2x+1 and 5x2−x+4, what is the highest degree term in the result?
If you solve: (3x2+2x−1)−(x3+3x+2), what would be the highest degree in the result?
cubic or 3
Define "degree" in relation to polynomials.
The greatest degree (largest exponent) of any term in the polynomial
Combine 2x2+3x−5+4x2−2x+1. What is the simplified polynomial?
6x2 + x - 4
Classify the polynomial x5−3x3+2x−1 in terms of both degree and number of terms.
quintic polynomial
Find the sum of (2x2+3x−5)+(x2−4x+7). Classify the final answer.
3x2 - x + 2 quadratic trinomial
If you subtract 3x+4 from 5x2+2, what is the resulting polynomial?
5x2 -3x -2