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

Front

What is the general form of a quadratic trinomial?

Back

The general form of a quadratic trinomial is ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the significance of the leading coefficient in a trinomial?

Back

The leading coefficient (a) determines the direction of the parabola when graphed and affects the factoring process.

Front

What is the first step in factoring a trinomial when a > 1?

Back

The first step is to multiply the leading coefficient (a) by the constant term (c) to find the product.

Front

How do you find two numbers that help in factoring a trinomial?

Back

You need to find two numbers that multiply to the product of a and c, and add up to b.

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What is the method of 'splitting the middle term' in factoring?

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Splitting the middle term involves rewriting the middle term (bx) as the sum of two terms that can be factored by grouping.

Front

What is the role of grouping in factoring trinomials?

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Grouping involves rearranging and grouping terms to factor by pairs, making it easier to find common factors.

Front

What is the difference between factoring a trinomial and a binomial?

Back

Factoring a trinomial involves three terms, while factoring a binomial involves only two terms.

Front

What is the purpose of checking your factors after factoring a trinomial?

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Checking your factors ensures that when multiplied, they return to the original trinomial, confirming the factorization is correct.