Algebra Review: Domain, Cancellation, Polynomials, Exponents & Radicals

A set of practice flashcards covering domain of rational expressions, polynomial cancellation, factoring and division, polynomial addition/subtraction, and exponent rules.

What is the domain of a rational expression?

All real numbers except those that make the denominator zero.

If the denominator is 4x - 4, what is the domain of the expression?

R \ {1} (all real numbers except x = 1).

What is the cancellation property for polynomials?

If p(x)s(x) = q(x)s(x) and s(x) ≠ 0, then p(x) = q(x).

Factor x^2 + 5x + 6.

(x+2)(x+3).

Divide x^2 + x − 6 by x + 3. What is the quotient?

Quotient is x − 2 (remainder 0).

Expand (x + 1)(x + 2).

x^2 + 3x + 2.

What does a^n mean?

a raised to the n-th power; multiply a by itself n times (a real number a and n a positive integer).

State the product rule for exponents.

a^n · a^m = a^{n+m}.

State the division rule for exponents.

a^n / a^m = a^{n−m}.

What is (ab)^n equal to?

(ab)^n = a^n b^n.

Compute (-2)^2.

4.

Compute (-3)^3.

-27.

Distribute 3(1 + 2m).

3 + 6m.