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 expressing it as a product of its factors, which are polynomials of lower degrees.

Front

What is the standard form of a quadratic trinomial?

Back

The standard form of a quadratic trinomial is ax^2 + bx + c, where a, b, and c are constants.

Front

How do you factor the trinomial x^2 + 5x + 6?

Back

(x + 2)(x + 3) is the factored form.

Front

What is the first step in factoring a trinomial?

Back

Identify the coefficients a, b, and c in the trinomial ax^2 + bx + c.

Front

What is the significance of the discriminant in factoring?

Back

The discriminant (b^2 - 4ac) determines the nature of the roots of the quadratic equation; if it's positive, there are two distinct real roots.

Front

Factor the trinomial 3x^2 + 12x + 12.

Back

3(x + 2)(x + 2) or 3(x + 2)^2.

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, e.g., (x + a)^2 = x^2 + 2ax + a^2.

Front

How do you factor the trinomial 4b^2 + 12b + 9?

Back

(2b + 3)(2b + 3) or (2b + 3)^2.

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.