Polynomials
Add/Subtract
Multiply
Factor
Oops all 600
100
Is the following a polynomial?
2 xx 2/(3*x^2)
Nope. The variable term has a negative exponent.
100
Add
(x^3+2x^2-5x+3)+(-x^3+2x-4)
2x^2-3x-1
100
Simplify:
6x(2x+3)
12x^2+18x
100
Factor
x^2+5x+6
(x+2)(x+3)
100
(2n+1)+(2n+3)+(2n+5) or 6n+9
200
Write the following polynomial in standard form:
7-3x^3+6x+5x^2
-3x^3+5x^2+6x+7
200
Subtract:
(2x^3-x^2+x-5)-(x^3-4x+3)
x^3-x^2+5x-8
200
Simplify:
(x+1)(x+2)
x^2+3x+2
200
Factor
2x^2+7x+6
(2x+3)(x+2)
200
p=3
300
What's the degree of the following polynomial?
3x-4x^5+9x^2-6x^3
The degree is five (it's the highest exponent).
300
Compute:
3(x^2-2x+2)+2(5x^2-x+4)
13x^2-8x+14
300
Multiply:
(3x-2)(x^2-x+1)
3x^3-5x^2+5x-2
300
Factor
49x^2+42x+9
(7x+3)^2
300
Factor
9-(k+3)^2
-k(k+6)
400
What's the leading coefficient of the following polynomial?
3x-4x^5+9x^2-6x^3
-4 (it's the coefficient of the term with the highest exponent)
400
Compute:
2(5x^2-x+3)-4(3x^2+7x+1)
-2x^2-30x+2
400
Compute:
(7x-2)^2
49x^2-28x+4
400
Factor
5x^4-80
5(x^2+4)(x+2)(x-2)
400
Factor:
a^2-b^2-10b-25
(a+b+5)(a-b-5)
500
Classify the following polynomial by number of terms and by degree:
7x^5-4x^3+x
It's a quintic (degree 5) trinomial (3 terms). If you couldn't remember the word "quintic" but said its degree is 5, then you can have 250 points.
500
Simplify:
(5y^2+3y-1)-(y^2-2y+3)+(2y^2+y+5)
6y^2+6y+1
500
Simplify
(5a-6b)(5a+6b)
25a^2-36b^2
500
Factor
x^3-7x^2+x-7
(x^2+1)(x-7)
500
Factor
x^3+3x^2y+3xy^2+y^3
(x+y)^3