Factoring 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 Greatest Common Factor (GCF)?

Back

The GCF is the largest factor that divides all the terms of a polynomial.

Front

How do you factor by grouping?

Back

To factor by grouping, you group terms with common factors, factor them out, and then factor the resulting polynomial.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What is the relationship between the roots and factors of a polynomial?

Back

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

Front

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

Back

To factor a trinomial of this form, 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 factoring case where a² - b² = (a + b)(a - b).

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.

Front

How do you factor a trinomial when a ≠ 1?

Back

When a ≠ 1, use the method of splitting the middle term or trial and error to find two numbers that multiply to ac and add to b.