Factoring completely

Front

What is factoring completely?

Back

Factoring completely is the process of breaking down a polynomial into the product of its simplest factors.

Front

What is the difference between a prime polynomial and a factorable polynomial?

Back

A prime polynomial cannot be factored into simpler polynomials with real coefficients, while a factorable polynomial can be expressed as a product of two or more polynomials.

Front

Factor completely: x⁸ - 16

Back

(x² + 2)(x² - 2)(x⁴ + 4)

Front

Factor completely: 9x² + 25

Back

prime

Front

Factor completely: x² – 8x – 8

Back

prime

Front

Factor completely: 8x³ - 18x

Back

2x(2x + 3)(2x - 3)

Front

Factor completely: x² - 2x - 15

Back

(x - 5)(x + 3)

Front

What is the first step in factoring a polynomial?

Back

The first step is to look for a common factor in all terms of the polynomial.

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern that states a² - b² = (a - b)(a + b).

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a) and is used to find the roots of a quadratic equation.