Factoring Completely

Front

What is factoring completely?

Back

Factoring completely is the process of breaking down an expression into its simplest factors, such that the expression cannot be factored any further.

Front

What is the first step in factoring a polynomial?

Back

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

Front

Factor the expression: 3x² - 15x + 18

Back

3(x-2)(x-3)

Front

What is a prime polynomial?

Back

A prime polynomial is a polynomial that cannot be factored into simpler polynomials with integer coefficients.

Front

Factor the expression: 50m³ - 2m

Back

2m(5m-1)(5m+1)

Front

What does it mean to factor by grouping?

Back

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

Front

Factor the expression: 15m² - 10m - 25

Back

5(m+1)(3m-5)

Front

What is the difference of squares?

Back

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

Front

Factor the expression: 8x³ - 18x

Back

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

Front

What is the quadratic formula?

Back

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