Sets & Intervals
This symbol means “belongs to” or “is an element of.”
What is ∈ ?
Use the product rule.
xᵐ · xⁿ = ?
Correct response:
What is xᵐ⁺ⁿ?
Classify by degree and number of terms.
7x⁴
Correct response:
What is a quartic monomial?
Factor out the GCF.
8x + 6
Correct response:
What is 2(4x + 3)?
Can the x be cancelled here?
x / (x + 4)
Correct response:
What is no?
x is not a factor of the entire denominator.
This is the smallest common number set containing −3. Choices: Natural, Whole, Integer, Irrational
Correct response:
What are the integers, Z?
Rewrite using a positive exponent.
x⁻³
What is 1/x³?
Identify the degree.
3x³ − 2x + 7
Correct response:
What is degree 3?
It is a cubic trinomial.
Factor the difference of squares.
x² − 16
Correct response:
What is (x − 4)(x + 4)?
Simplify and state restrictions.
x²/[x(x + 4)]
Correct response:
What is x/(x + 4)?
Restrictions: x ≠ 0, −4
Write this inequality in interval notation.
32 < x < 112
Correct response:
What is (32, 112)?
Rewrite the radical using a fractional exponent.
√x
Correct response:
What is x¹ᐟ²?
This expression is polynomial, rational, or algebraic?
1/x
Correct response:
What is a rational expression
Factor the perfect-square trinomial.
x² − 10x + 25
Correct response:
What is (x − 5)²?
Simplify using opposite factors.
(9 − x²) / (x − 3)
Correct response:
What is −(x + 3)?
Restriction: x ≠ 3
This set operation means “and” or “overlap.”
Correct response:
What is intersection, ∩?
Simplify the radical.
√18
Correct response:
What is 3√2?
True or false: irrational numerical coefficients automatically make an expression non-polynomial.
Example: √2x + 3
Correct response:
What is false?
√2x + 3 is still a polynomial.
Factor using the AC method.
2x² + 5x − 3
Correct response:
What is (2x − 1)(x + 3)?
Rationalize the denominator.
5/√3
Correct response:
What is 5√3 / 3?
Simplify the interval expression.
(1, 5) ∩ [3, ∞)
Correct response:
What is [3, 5)?
Simplify using exponent rules.
(x²)³ / x⁴
Correct response:
What is x²?
Classify the expression.
(5x³ − 1) / (x² + 7x − 2)
Correct response:
What is a rational expression, but not a polynomial?
Factor completely using quadratic-form substitution.
x⁶ − 9x³ + 8
Correct response:
What is
(x − 1)(x² + x + 1)(x − 2)(x² + 2x + 4)?
Simplify the compound fraction.
((x/3) + (y/4)) / (1/12)
Correct response:
What is 4x + 3y?