Definitions
What is a number or variable in a polynomial that is separated by an addition or subtraction sign
a term
Add the Polynomials
(4x + 9) +(x - 4)
5x + 5
Subtract the polynomials:
(g - 4) - (3g - 6)
-2g + 2
3(3x)
9x
(x + 6) (x + 3)
x2 +9x +18
x2 - 9
(x+3)(x-3)
The degree of this polynomial:
x3 - 7x2 + 4x5 - 19x7
7
Find the area of a room that is (3x - 5) ft by (2x + 1) ft.
6x2 - 7x - 5 ft2
This type of product excludes the middle term
Difference of squares
DAILY DOUBLE
The number before a variable within a term is called the...
Coefficient
Add the polynomials:
(-3a - 2) + (7a + 5)
4a + 3
Subtract the polynomials:
(-5h - 2) - (7h +6)
-12h - 8
Multiply the Polynomials:
(3x)(2y)
6xy
(3x - 4)(2x + 5)
6x2 + 7x - 20
What is the GCF of the following:
- 3x2 - 3x - 60
-3 or 3
Classify by its degree and number of terms:
10x
Linear Monomial
DAILY DOUBLE
What are the dimensions of a rectangular prism with a volume of 15x3+ 52x2+ 32x?
(x)(5x + 4)(3x + 8)
This product includes a middle term and has perfect squares for the first and last term.
Perfect Square Trinomial
The number in front of the term with the highest exponent.
Leading Coefficient
Add the polynomials:
(x2 +3x + 5) + ( -x2 +6x)
9x + 5
Subtract the polynomials:
(-x2 - 5) - (-3x2 -x -8)
2x2 + x +3
Multiply the Polynomials:
3x2 (2x4 + 4)
6x6 + 12x2
(x - 8)(2x + 3)
2x2 - 13x - 24
Factor completely.
4x2 - 2x + 24
(4x - 6)(x + 4)
A constant polynomial has a degree of this.
0
What are the dimensions of a rectangular prism with a volume of 18x3+ 84x2+ 48x?
(6d)(3d + 2)(d + 4)
Factorising a trinomial leads two a product of two of these
Binomials
The highest exponent on the variables in a term
Degree of the term
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
4x(x-2)^2
4x^3-16x^2+16x
(y + 9) (y + 9)
y2 + 18y + 81
Find the length and width of a square with an area of
9x2+48x+64
(3x+8)(3x+8)
Rewrite this polynomial in standard form
-6a4 + 10a3 + 14a7 - 22a2 + 33
14a7 - 6a4 + 10a3 -22a2 +33
A storage bin in the shape of a rectangular prism has a volume of 10x3+ 9x2+ 2x. What linear expressions can represent possible dimensions of the bin?
x, 5x + 2, 2x + 1
When looking at the area model, one observation about the across from each other includes that the ______________ are equal.
cross products
Terms that have the same variables and the same degree are....
Like terms
Add the polynomials:
(-1 + x2 + 2x) + (1 -2x + 2x2)
3x2
Subtract the Polynomials:
(2x2 - 3x) - (x2 -2x + 4)
x2 + x - 4
(2x-3y+6)(3y)
6xy-9y2+18y
(x - 12)(x + 12)
x2 - 144
Factor completely.
32x2+24x-80
8(x + 2)(4x - 5)
Refers to the highest exponent in a polynomial, or the exponent on a specific term
Degree
What are the dimensions of a rectangular prism with a volume of 32x3+ 224x2+ 360x?
(8x)(2x - 5)(2x - 9)
When using algebra tiles to factor a polynomial the goal is to create this
Rectangle, find the length and width.