Factoring Trinomials a>1

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What is a trinomial?

Back

A trinomial is a polynomial that consists of three terms, typically in the form ax² + bx + c.

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What does it mean to factor a polynomial?

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

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What is the standard form of a quadratic trinomial?

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

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

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

Front

How do you factor a trinomial when a = 1?

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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).

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What is the method of grouping in factoring?

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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.

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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.

Front

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

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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?

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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.