Vocab
A number and a Variable
What is a Term
The degree of this polynomial:
x3 - 7x2 + 4x5 - 19x7
.
7
Add the Polynomials
(4x + 9) +(x - 4)
5x + 5
Subtract the polynomials:
(g - 4) - (3g - 6)
-2g + 2
Multiply the Polynomials:
3x2 (2x4 + 1)
6x6 + 3x2
A Polynomial with two Terms
Binomial
Classify by its degree and number of terms:
10x20
20 degree monomial
Add the polynomials:
(-3a - 2) + (7a + 5)
4a + 3
Subtract the polynomials:
(-5h - 2) - (7h +6)
-12h - 8
Multiply the Polynomials:
3x(2x + 4x2 - 5)
12x2 + 6x3 - 15x
Ordered Alphabetically and with the highest Variable First
What is Standard Form
Tell me the type of Polynomial based on the number of terms.
3x + 2y + 4
What is a Trinomial
Add the polynomials:
(x2 +3x + 5) + ( -x2 +6x)
9x + 5
Subtract the polynomials:
(-x2 - 5) - (-3x2 -x -8)
2x2 + x +3
Multiply the Polynomials:
−y2 (−8x2 − 6xy − y2 )
8y2x2 + 6y3x + y4
Key word/Action when Multiplying Monomials to any Polynomial
What is Distribution
Rewrite this polynomial in standard form (hint, highest degree first)
-6a4 + 10a3 + 14a7 - 22a2 + 33
14a7 - 6a4 + 10a3 -22a2 +33
Add the polynomials:
(t2 + 3t3 -3) + (2t2 +7t -2t3)
t3 +3t2 +7t -3
Subtract the Polynomials:
(k2 + 6k3 -4) - (5k3 + 7k -3k2)
k3 + 4k2 -7k -4
Multiply the Polynomials:
(7r6s7tu)(9r8s2tu8)
63r14s9t2u9
The Acronym Used to Multiply two Binomials
What is FOIL. (First Outer Inner Last)
Classify by Number of terms and Degree:
6x3 - 4x2 + 2x + 5
What is a Cubic Polynomial
Add the polynomials:
(-1 + x2 + 2x) + (1 -2x + 2x2)
3x2
Subtract the Polynomials:
(2x - 3x) - (x2 -2x + 4)
-x2 + x - 4
Multiply the Polynomials:
(3x + 1)(x - 4)
3x2 - 11x - 4
Refers to the highest exponent in a polynomial, or the exponent on a specific term
Degree
Terms that have the same variables and the same degree are....
Like terms
Find the sum of the following sides of a triangle (perimeter) (3x + 10), (x + 5), (x + 10)
5x + 25 units
Subtract the following polynomials
(3 - 6x5 - 8x4) - (-6x4 - 3x - 8x5)
2x5 - 2x4 + 3x + 3
Multiply the following polynomials
(3r2 + 5)2
9r4 + 30r2 + 25