Factoring Trinomials (a not 1)

Front

What is a trinomial?

Back

A trinomial is a polynomial that consists of three terms, typically in the form ax² + 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 Greatest Common Factor (GCF)?

Back

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

Front

How do you factor out the GCF from a polynomial?

Back

To factor out the GCF, identify the largest common factor of all terms and divide each term by this factor, then write it outside the parentheses.

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

What is the process for factoring a trinomial when a ≠ 1?

Back

To factor a trinomial where a ≠ 1, find two numbers that multiply to ac and add to b, then rewrite the middle term and factor by grouping.

Front

What is the significance of the leading coefficient in factoring?

Back

The leading coefficient (a) affects the shape of the parabola represented by the trinomial and influences the factoring process.

Front

What is the difference between factoring by grouping and factoring using the quadratic formula?

Back

Factoring by grouping involves rearranging and grouping terms to find factors, while the quadratic formula provides a direct solution for finding roots.

Front

How do you check if your factorization is correct?

Back

To check if the factorization is correct, multiply the factors back together and see if you obtain the original polynomial.

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.