Laws of Exponents
Division
Polynomials
Factor Polynomials
100
Simplify:
a^-4b^3c^0
(b^3)/a^4
100
What is the original polynomial?
3x^3-10x^2-5
100
Identify the degree, leading coefficient and end behavior
2x^2+3x-1
Degree 2, Leading Coefficient 2
End behavior
"x --> " oo", f(x) --> "oo
"x --> " -oo", f(x) --> "oo
100
Write the expression in quadratic form if possible.
2x^6+3x^3-1
2(x^3)^2+3(x^3)-1
Or
u=x^3
2u^2+3u-1
200
Simplify:
(5^-3/(2*5^-4x^2))^(2)
25/(4x^4)
200
Divide
(x^3-4x^2+9)/(x-3)
x^2-x-3
200
Simplify the following expression (write your answer in descending order of degrees)
(5 + 7x^3 + 3x^2)+(-12 +5x + 6x^2)
7x^3 + 9x^2 + 5x -7
200
Factor by grouping
x^3+2x^2-3x-6
(x+2)(x^2-3)
300
Simplify:
(7x^3)^2*(x^4)^(3)
49x^18
300
Divide
(x^3+1)/(x+1)
x^2-x+1
300
Identify the degree, leading coefficient and end behavior
-5x^7+4x^2+3x-5
Degree: 7
Leading Coefficient: -5
End behavior
"x --> " oo", f(x) --> "-oo
"x --> " -oo", f(x) --> "oo
300
Factor with the sum or difference of cubes
8x^3+1
(2x+1)(4x^2-2x+1)
400
Simplify:
((1/3)xz^3)^2
(x^2z^6)/9
400
Divide
(3x^6-7x^5-53x^3-26x^2-43x-34)/(3x+2)
x^5-3x^4+2x^3-19x^2+4x-17
400
Simplify
(-10mn^3-4n^4)-(-2n^4-7mn^3)-(5n^3+6mn^3)
-9mn^3-2n^4-5n^3
400
Factor completely
x^4+3x^3-4x^2-12x
x(x+3)(x-2)(x+2)