Review of Unit 2B

Front

Factor: 4x^2 - 25

Back

(2x + 5)(2x - 5) - This is a difference of squares, which can be factored as a^2 - b^2 = (a + b)(a - b).

Front

Factor: 64 - 27a^3

Back

(4 - 3a)(9a^2 + 12a + 16) - This is a difference of cubes, which can be factored using the formula a^3 - b^3 = (a - b)(a^2 + ab + b^2).

Front

Factor completely: x^4 - 10x^2 + 9

Back

(x + 3)(x - 3)(x + 1)(x - 1) - This can be factored by recognizing it as a quadratic in terms of x^2.

Front

Factor: x^4 - 81

Back

(x^2 + 9)(x - 3)(x + 3) - This is a difference of squares, where x^4 - 81 = (x^2 - 9)(x^2 + 9).

Front

Factor: x^3 - 343

Back

(x - 7)(x^2 + 7x + 49) - This is a difference of cubes, where 343 = 7^3.

Front

Definition: Difference of Squares

Back

A difference of squares is an expression of the form a^2 - b^2, which can be factored as (a + b)(a - b).

Front

Definition: Difference of Cubes

Back

A difference of cubes is an expression of the form a^3 - b^3, which can be factored as (a - b)(a^2 + ab + b^2).

Front

Definition: Perfect Square Trinomial

Back

A perfect square trinomial is an expression of the form a^2 ± 2ab + b^2, which can be factored as (a ± b)^2.

Front

Definition: Factoring by Grouping

Back

Factoring by grouping involves rearranging and grouping terms in a polynomial to factor it into simpler polynomials.

Front

Example: Factor x^2 - 5x + 6

Back

(x - 2)(x - 3) - This is a quadratic that can be factored by finding two numbers that multiply to 6 and add to -5.