EQUATIONS
10x+20y
what is...
10(x+2y)
Monomial
A polynomial with just one term
Is this a polynomial identity (x + y)² = x² + 2xy + y²
What is Yes
x2-9
(x-3)(x+3)
Will the line of a polynomial always be smooth and curvy?
Yes, it will
35a+7b-14c
7(5a+b-2c)
Binomial
A polynomial with exactly two terms, which may or may not be like terms.
What is a polynomial identity
A polynomial identity is a mathematical equation involving polynomials that is always true, essentially, it's an equation where both sides are equal no matter what value you plug in.
x2+6x+9
(x+3)(x+3) or (x+3)2
If the graph of a polynomial have even multiplicity, where will is touch on the horizontal axis?
2a3−4a2+3a−1+(a3+2a2−a+5)
3a3−2a2+2a+4
Polynomial Function
An expression with terms that have numbers and variables, where the variables have whole number exponents
Is this a polynomial identity x² + y² = (x + y)²
Not a polynomial identity
x2−5x−14
(x−7)(x+2)
What happens if the degree of a polynomial is odd?
The line of the graph will go up and down, not both in the same direction.
3x4−2x3+x2+5−(x4−3x2+2)
2x4−2x3+4x2+3
Factorable Polynomial
A polynomial that can be written as the product of two or more simpler polynomials
Is this a polynomial identity 1/x + 1/y
What is no
4x2−25
(2x−5)(2x+5)
True or false- The degree of a polynomial effects what the graph's line shape looks like.
True
4x5−3x3+2x2−7x+5+x5−4x3+3x2−2x−1
5x5−7x3+5x2−9x+4
Polynomial Division
The process of dividing one polynomial by another polynomial, often used to find the quotient and remainder
Is this a polynomial identity
(x + a)(x + b) = x² + x(a + b) + ab
What is yes
3x2+11x−4
(3x−1)(x+4)
Does the graph of a polynomial turn directions at its changing point?
Yes, it does.