Sums and differences of squares and cubes
This expression can be factored using the identity
a2 - b2=(a - b)(a + b):
x2 - 49
What is:
(x-7)(x+7)
Factor out the greatest common factor from this expression:
6x2 + 9x
What is 3x(2x + 3)
These are both the solutions to the square root of -81
What is 9i and -9i
This is the number of real solutions to the equation if I use the discriminant:
2x2 -5x +18 = 0
What is no real solutions
-119
This point is the local minima for
f(x) = -x3 + 3x2
What is (2,4)
Though it cannot be factored over real numbers, it does have these imaginary solutions:
x2+36=0
What is :
x= 6i and -6i
Factor this quadratic trinomial:
4x2 + 28x + 48
What is 4(x + 3)(x + 4)
Simplify the term i17
What is i
The zeros for this equation are...
-3x2 +6x + 24 = 0
What are
x = 4 and 2
As x approaches -∞, what is the end behavior of
f(x) = -4x3 + 2x
What is ∞
Use the identity a3 - b3 = (a - b)(a2 + ab + b2) to factor this expression:
8x3 - 27
What is (2x - 3)(4x2 +6x + 9)
Use the identity for difference of squares to factor:
25x2 − 4
What is (5x − 2)(5x + 2)
Simplify (2 - 3i)(6 + 5i)
What is 27 - 8i
These are the zeros that I see on the graph of
f(x) = x3 + x - 12
What are 0, 3, -4
This would be the range of
f(x) = 2x2 + 4x - 6 when written in interval notation.
What is [-8, ∞ )
Apply the formula a3 + b3 = (a + b)(a2 - ab +b2) to factor:
x3 + 64
What is (x + 4)(x2 - 4x + 16)
Factor this quadratic:
6x2 − x − 2
What is (3x + 2)(2x − 1)
This is the simplified version of the expression:
9 - 6i - (4 + 3i)
What is 5 - 9i
This would be the zeros that have multiplicity according to the graph of the polynomial:
x5 + 3x4 - 4x2
What are 0 and -2
This is the interval of decrease, in interval notation, for
f(x) = 2x3 - 6x2 +5
What is (0, -3)
This is equation will yield these four x-values:
x4 - 16
What are x= -2, 2, -2i, 2i
Use grouping to factor the polynomial completely:
x3 + 3x2 - 25x − 75
What is (x − 5)(x+5)(x + 3)
This is the complex solution to the equation below using the quadratic formula. Make sure to simplify both radicals and fractions.
5x2 - 4x + 2 = 0
What is:
2 +- i square root 6 over 10
This is the only root of the function below that has a multiplicity of 2.
f(x) = 3x4 - 33x3 + 16x2 + 70x - 30
What is 1.
The roots were 1 (mult. of 2), -2/3 and 5
Written in interval notation, this is the domain and range of
-3x4 + x3 + 2x2 +5x - 4
What is ( -∞ , ∞ ) for the domain
( -∞ , 1] for the range