How do you add or subtract polynomials?	Combine like terms (same variable and exponent). Example: (3x^2 + 2x) + (x^2 - 5x) = 4x^2 - 3x.
How do you multiply two binomials using FOIL?	First, Outer, Inner, Last. (a + b)(c + d) = ac + ad + bc + bd. Example: (x + 3)(x - 2) = x^2 - 2x + 3x - 6 = x^2 + x - 6.
What is the difference of squares formula?	a^2 - b^2 = (a + b)(a - b). Recognize this pattern to factor quickly.
What is a perfect square trinomial?	a^2 + 2ab + b^2 = (a + b)^2 or a^2 - 2ab + b^2 = (a - b)^2.
How do you simplify expressions with exponents when multiplying?	Add the exponents: x^a * x^b = x^(a+b). Example: x^3 * x^4 = x^7.
How do you simplify expressions with exponents when dividing?	Subtract the exponents: x^a / x^b = x^(a-b). Example: x^5 / x^2 = x^3.
What does a negative exponent mean?	x^(-n) = 1/x^n. A negative exponent flips the base to the denominator.
What does a fractional exponent mean?	x^(m/n) = the nth root of x^m. Example: 8^(2/3) = (cube root of 8)^2 = 2^2 = 4.
How do you solve a radical equation like sqrt(x + 5) = 3?	Square both sides: x + 5 = 9, so x = 4. Always check by plugging back in: sqrt(4 + 5) = sqrt(9) = 3. It works.
What is a complex number?	A number in the form a + bi, where i = sqrt(-1). Example: 3 + 2i. The SAT tests basic operations with complex numbers.
What is i^2?	i^2 = -1. This is the defining property of the imaginary unit.
How do you find the remainder when dividing polynomials?	Use the Remainder Theorem: the remainder of f(x) / (x - a) equals f(a). Plug in the value instead of doing long division.
What is the end behavior of a polynomial with a positive leading coefficient and even degree?	Both ends go up (toward positive infinity). As x goes to positive or negative infinity, f(x) goes to positive infinity.
How do you solve an exponential equation like 2^x = 16?	Rewrite both sides with the same base: 2^x = 2^4, so x = 4. If bases don't match, use logarithms.
What is exponential growth vs. exponential decay?	Growth: y = a(1 + r)^t where r > 0. Decay: y = a(1 - r)^t where 0 < r < 1. The base determines direction.
How do you solve a rational equation like 1/x + 1/3 = 1/2?	Find the LCD (6x), multiply every term by it, then solve the resulting equation. Check that your answer does not make any denominator zero.
What are the zeros of a polynomial?	The x-values where the polynomial equals zero (where the graph crosses or touches the x-axis). Found by setting f(x) = 0 and solving.
How do you solve absolute value equations like |2x - 1| = 7?	Set up two cases: 2x - 1 = 7 (so x = 4) and 2x - 1 = -7 (so x = -3). Both are valid solutions.
What is the vertex form of a quadratic?	y = a(x - h)^2 + k, where (h, k) is the vertex. If a > 0, the parabola opens up; if a < 0, it opens down.
How does completing the square work?	For x^2 + bx, add (b/2)^2 to create a perfect square trinomial. Example: x^2 + 6x becomes x^2 + 6x + 9 = (x + 3)^2. Remember to balance both sides.