Polynomials And Equations

For any numbers x

For any numbers x, a, b: (x + a)(x + b) = x² + (a + b)x + ab. This fundamental identity helps us multiply first-degree polynomials systematically. Exa

The reverse process of multiplication

The reverse process of multiplication - breaking a second-degree polynomial into two first-degree factors. To factorize x² + bx + c, we find numbers p

If (x

If (x - p)(x - q) = 0, then either x - p = 0 or x - q = 0, giving x = p or x = q. This zero product property allows us to solve quadratic equations by

For polynomials difficult to factorize mentally

For polynomials difficult to factorize mentally, use: if a + b = s and ab = p, then (a - b)² = s² - 4p. Example: For x² + 27x + 180, we have s = 27, p

For ax² + bx + c

For ax² + bx + c = 0, the solutions are x = (-b ± √(b² - 4ac))/(2a). The expression b² - 4ac is called the discriminant. Example: For 2x² + 3x - 2 = 0