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Factoring
★★☆☆☆Middle School
📖Definition
Expressing a polynomial as a product of two or more polynomials.
📐Formulas
a² - b² = (a+b)(a-b)
Difference of squares
a² + 2ab + b² = (a+b)²
Perfect square trinomial (addition)
a² - 2ab + b² = (a-b)²
Perfect square trinomial (subtraction)
x² + (a+b)x + ab = (x+a)(x+b)
Factoring quadratic trinomials
a³ + b³ = (a+b)(a² - ab + b²)
Sum of cubes
a³ - b³ = (a-b)(a² + ab + b²)
Difference of cubes
✏️Examples
예제 1★★☆☆☆
Factor x² - 9.
x² - 9 = (x+3)(x-3)
예제 2★★☆☆☆
Factor x² + 5x + 6.
x² + 5x + 6 = (x+2)(x+3)
예제 3★★★☆☆
Factor 2x² + 7x + 3.
⚡Applications
Solving equations
Solving quadratics by factoring
Simplifying fractions
Reducing algebraic fractions
#algebra#polynomial#factoring#fundamental