🧮 Algebra

Explanation: log??(1000) = log??(10³) = 3. Logarithm is the inverse of exponentiation: 10³ = 1000, so log??(1000) = 3.

Explanation: The discriminant of a quadratic ax² + bx + c is D = b² - 4ac. If D > 0, two real roots; D = 0, one repeated root; D < 0, no real roots.

Explanation: Polynomials are named by degree: degree 1 = linear, degree 2 = quadratic, degree 3 = cubic, degree 4 = quartic, degree 5 = quintic.

Explanation: A quadratic equation has the form ax² + bx + c = 0. y = x² + 4x + 4 is quadratic (highest power is 2). Linear has power 1; cubic has power 3.

Explanation: 2x + 3 = 11 ? 2x = 11 - 3 ? 2x = 8 ? x = 4. Always subtract constants from both sides first, then divide.