Factoring Trinomials

Front

What is a trinomial?

Back

A trinomial is a polynomial that consists of three terms, typically in the form ax^2 + bx + c.

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means to express it as a product of its factors, which are polynomials of lower degrees.

Front

What is the difference of squares formula?

Back

The difference of squares formula states that a^2 - b^2 = (a + b)(a - b).

Front

How do you factor the trinomial x^2 + bx + c?

Back

To factor x^2 + bx + c, find two numbers that multiply to c and add to b, then express it as (x + m)(x + n) where m and n are those numbers.

Front

What is the first step in factoring a trinomial?

Back

The first step in factoring a trinomial is to identify the coefficients of the terms and check if there is a common factor.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a trinomial that can be expressed as the square of a binomial, in the form (a + b)^2 or (a - b)^2.

Front

How do you factor the expression 4x^2 - 25?

Back

4x^2 - 25 can be factored using the difference of squares formula: (2x + 5)(2x - 5).

Front

What is the significance of the leading coefficient in factoring?

Back

The leading coefficient affects the shape and direction of the parabola represented by the trinomial, and it may need to be factored out before applying other factoring techniques.

Front

What is the method of grouping in factoring?

Back

The method of grouping involves rearranging and grouping terms in a polynomial to factor by common factors.

Front

What is the factored form of x^2 - 144?

Back

The factored form of x^2 - 144 is (x + 12)(x - 12), using the difference of squares formula.