Vocab #1
A number, variable, or a product of a number and a variable in a polynomial that is separated by an addition or subtraction sign is called a ...
a term
The degree of this polynomial:
x3 - 7x2 + 4x5y2 - 19x7y
- 19x7y1
Add the exponents from the variables 7 + 1 = 8
Final Answer = 8
Add the Polynomials
(4x - 9) + (x + 4)
5x - 5
a^6+8a^4-9+7a^6+2
8a^6+8a^4-7
-9xy^4(4xy^2-7)
-36x^2y^6+63xy^4
The number before a variable within a term is called the...
Coefficient
Write in standard form
2x + 3x2 - 5
3x2 + 2x - 5
Add the polynomials:
(-3ab - 12) + (7ab + 5)
4ab - 7
5xyz - 9x + 3y - 8xyz + 9x
-3xyz+3y
(5x-3)2
25x^2-30x+9
The number in front of the term with the highest degree.
Leading Coefficient
A cubic polynomial has a degree of this.
Subtract the polynomials:
(-x2 - 5) - (-3x2 -x -8)
(-1x2 - 5) + (3x2 + 1x + 8)
Final Answer: 2x2 + x + 3
xy + 2x^2 - 2xy + 8y^2
2x^2+8y^2-xy
Multiply the Polynomials:
(3x2 +4x)(2x5 + 6y)
6x^7+8x^6+18x^y+24xy
When you add the exponents of each of the variables of each term and found the highest one you found the...
Degree of the term
Classify by degree and number of terms:
7x^2+8x
Quadratic binomial
Subtract the Polynomials:
(k2 + 6k3 -4) - (5k3 + 7k -3k2)
Change to addition problem and combine like terms.
(1k2 + 6k3 -4) + (-5k3 - 7k +3k2)
k3 + 4k2 -7k - 4
7a +6 - 6a - 5a - 4a + 4
-8a+10
(2x-3)(2x+3)
4x2 +6x - 6x - 9
Final Answer: 4x2 - 9
Terms that have the same variables and the same degree are called ...
Like terms
Which of the following are examples of a monomial?
a) 2x - 3x
b) 3x - 9y
c) 9x2 - 2x
d) 1 + 2 + 9
A) 2x - 3x = -1x
and
D) 1 + 2 + 9 = 12
Subtract the Polynomials:
(2x2 - 3x) - (x2 -2x + 4)
Change subtraction to addition
(2x2 - 3x) + (-1x2 +2x - 4)
x2 - x - 4
-9x^2y^9+2x^2y+2xy^2-8x^2y+8x^2y^9
-x^2y^9-6x^2y+2xy^2
(3x-4)(8x^2+7x-8)
24x^3-11x^2-52x+32