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 equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.

Front

What is the relationship between the roots of a quadratic equation and its factors?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero, and they correspond to the factors of the polynomial.

Front

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

Back

To factor a trinomial of the form 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 difference of squares?

Back

The difference of squares is a special factoring case where a^2 - b^2 can be factored as (a - b)(a + b).

Front

How do you factor a trinomial when a is not equal to 1?

Back

When a is not equal to 1, use the method of grouping or trial and error to find two binomials that multiply to the trinomial.

Front

What is the significance of the leading coefficient in factoring?

Back

The leading coefficient affects the shape of the parabola represented by the quadratic and influences the factoring process.

Front

What is the FOIL method in relation to factoring?

Back

The FOIL method is a technique used to multiply two binomials, which can also help in reverse engineering the factors of a trinomial.

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, such as (a + b)^2 = a^2 + 2ab + b^2.