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 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 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.

Tags

CCSS.HSF-IF.C.7A

Front

How do you factor a trinomial when a = 1?

Back

When a = 1, you look for two numbers that multiply to c and add to b, then express the trinomial as (x + m)(x + n).

Front

What is the method of grouping in factoring?

Back

The method of grouping involves rearranging and grouping terms in a polynomial to factor it into simpler polynomials.

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What is the difference between factoring completely and factoring partially?

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Factoring completely means breaking down a polynomial into its simplest factors, while factoring partially may leave some factors intact.

Front

What is a perfect square trinomial?

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A perfect square trinomial is a trinomial that can be expressed as the square of a binomial, such as (a + b)² = a² + 2ab + b².

Tags

CCSS.HSA.APR.C.4

Front

How do you factor a trinomial of the form ax² + bx + c?

Back

To factor a trinomial of the form ax² + bx + c, find two numbers that multiply to ac and add to b, then use these to split the middle term.

Front

What is the role of the discriminant in factoring quadratics?

Back

The discriminant (b² - 4ac) determines the nature of the roots of a quadratic equation and can indicate if it can be factored over the reals.

Tags

CCSS.HSA-REI.B.4B