Question

Factor the trinomial. $$ b^{2}+5 b-24 $$

   Factor the trinomial.
$$
b^{2}+5 b-24
$$

Algebra 1: Concepts and Skills

Algebra 1: Concepts and Skills

Ron Larson, Laurie… 1st Edition

Chapter 10, Problem 17

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Solved by Expert Cory Kuzinski

04/20/2020

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Factor the trinomial. $$ b^{2}+5 b-24 $$

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Key Concepts

The AC Method

The AC method is a systematic approach to factoring quadratic trinomials when the leading coefficient a is not equal to one. It involves multiplying the leading coefficient a with the constant term c to find a product, then finding two numbers that multiply to this product and add to the middle coefficient b. Once these numbers are identified, the middle term is split accordingly, and factoring by grouping can be performed.

Quadratic Trinomials

A quadratic trinomial is a polynomial expression of the form ax² + bx + c. Factoring it involves expressing the trinomial as a product of two binomials. This process requires an understanding of how the coefficients a, b, and c interact, and how they can be split into factors that combine to form the original expression.

Factor Pair Identification

Factor pair identification is a crucial step in factoring trinomials, where one seeks two numbers that both multiply to a specific product (usually a * c) and sum to the middle coefficient b. This technique leverages knowledge of how pairs of factors interact and is essential not only for the AC method but also for simpler cases where the leading coefficient is one.

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