Factoring (Quadratics & Cubics) - Final Exam Review

Factoring is the process of breaking down an expression into a product of simpler expressions, or factors, that when multiplied together give the original expression.

A quadratic polynomial is a polynomial of degree 2, typically in the form $$ax^2 + bx + c$$ . A cubic polynomial is of degree 3, typically in the form $$ax^3 + bx^2 + cx + d$$ .

$$(x + 7)(x - 7)$$ (Difference of squares)

$$(x - 3)(x^2 + 3x + 9)$$ (Difference of cubes)

$$(x - 13)(x + 8)$$ (Factoring a quadratic)

$$(x + 2)(x^2 - 2x + 4)$$ (Sum of cubes)

The formula is $$a^2 - b^2 = (a + b)(a - b)$$ .

The formula is $$a^3 + b^3 = (a + b)(a^2 - ab + b^2)$$ .

The formula is $$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$$ .

$$(x^2 + 5)(x - 5)$$ (Factoring by grouping)