Addition of Polynomials
Subtraction of Polynomials
Monomial Multiplication
Multiplying Polynomials
Mixed Review
A little bit of everything
100
(4x2 + 2x) + (x2 + 6x)
5x2 +8x
100
(y2 - 10xy) - (2y2 + 3xy)
-y2 -13xy
100
(6x2)(5x)
30x3
100
(x + 4)(x - 2)
x2 + 2x - 8
100
Which property allows you to change where the parentheses are?
Associative Property
100
Adding, subtracting and multiplying polynomials is a closed set. Integers are also the same. What does this mean?
When the polynomial operations are addition, subtraction and/or multiplication, the result will ALWAYS be a polynomial. This is the also true of integers.
200
(-3y2 + y) + (4y2 + 6y)
y2 +7y
200
(2x^2+5x-3)-(3x^3+2x-5)
-3x3 + 2x2 +3x + 2
200
(x2yz)(x2y4)
x4y5z
200
(a + 3)(a − 2)
a2 + 1a − 6
200
Which property allows you to change the order?
Communative Property
200
A square has a side length of
x -3.
What is the area of the square?
x^2-6x+9
300
(2a^2-7a+10)+(a^2+4a+7)
3a2 -3a +17
300
(4-x-2x^2)-(-2+3x-x^3)
x3 - 2x2 - 4x + 6
300
How many terms are in a monomial?
One
300
(4m + 2)(4m + 5)
16m2 + 28m + 10
300
Which expression is not a polynomial?
D, if there is a variable in the polynomial, the exponent associated with that variable must always be an INTEGER ≥ 0.
300
Explain why the following expression is not a polynomial.
3x^2 + sqrt(2x) - 9
The expression is not a polynomial because the variable is under the square root symbol. Therefore, the variable has an exponent of 1/2. All polynomials that have a variable must have an exponent that is a positive INTEGER ≥ 0.
400
A triangle has the following side lengths:
2r2 - 5r + 7
3r3 - 6r
r - 5
What is the perimeter of the triangle?
3r3 + 2r2 -10r + 2
400
The area of polygon A is 3a2 - 2a (when a>1) The area of polygon B is 4a - 4. (when a>0)
What is the difference in area from Polygon A to Polygon B?
3a2 - 6a + 4
400
2x(x + 6)
2x2 + 12x
400
(5b − 6)(5b2 + 4b − 2)
25b3 − 10b2 − 34b + 12
400
Simplify the following:
3x^2 + 4 - 3(x^2 - 2)
10
400
Simplify
4x(x-1)^2
4x^3-8x^2+4x
500
The width of the rectangle is two less than three times the height of the rectangle. Write a simplified expression for the perimeter of the rectangle.
8x - 4
500
A height of ball being thrown in the air at 20 ft per second with a starting height of 6 ft can be modeled with the expression -16t2+20t +6. (t = time in seconds)
The expression when the speed is 30 ft per second and starts at 4 ft is -16t2 + 30t + 4
What is the difference in the height of the two after t seconds?
-10t + 2
Follow up: At what time, will the balls be at the same height? (Hint, the difference in height between the two balls will be 0.)
500
A rectangle has a width of 2x and a height of 4x. What is the area of the rectangle?
8x2
500
The height of a triangle is 8n2 + n − 4.
The base of a triangle is 6n2 − 6n − 4.
What is the area of the triangle?
24n4 − 21n3 − 31n2 + 10n + 8
500
How many terms are in a binomial?
Two
500
Which expressions will result in a trinomial when simplified?
A. 9x2 - 30x + 25
D. x2 + x + 4
E. 8x2 + 6x - 9