Factor Trinomials

Front

What is a trinomial?

Back

A trinomial is a polynomial with three terms, typically in the form ax² + 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 ax² + bx + c, where a, b, and c are constants.

Front

How do you factor a trinomial of the form x² + bx + c?

Back

To factor x² + bx + c, find two numbers that multiply to c and add to b, then express it as (x + m)(x + n).

Front

What is the difference of squares?

Back

The difference of squares is a special case of factoring, expressed as a² - b² = (a + b)(a - b).

Front

What is the process for factoring by grouping?

Back

Factoring by grouping involves rearranging terms and factoring out common factors from pairs of terms.

Front

What is the significance of the leading coefficient in factoring?

Back

The leading coefficient (the coefficient of the highest degree term) affects the methods used for factoring and the final factors.

Front

How do you factor a trinomial when a ≠ 1?

Back

When a ≠ 1, use the method of trial and error or the AC method, where you multiply a and c, then find factors that add to b.

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., (a + b)² = a² + 2ab + b².

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.