Question

Factor the trinomial. $6 x^{2}-7 x-20$

   Factor the trinomial.
$6 x^{2}-7 x-20$

Algebra and Trigonometry

Algebra and Trigonometry

Judith A. Beecher,… 4th Edition

Chapter 0, Problem 38

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Solved by Expert Ankit Gupta

07/06/2020

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Those numbers are -10 and 12. Show more…

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Factor the trinomial. $6 x^{2}-7 x-20$

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Key Concepts

Factor by Grouping

Factor by Grouping is a strategy often used in conjunction with the AC Method. After splitting the middle term of a quadratic trinomial, the terms can be arranged into pairs, with each pair having a common factor. Factoring out the common factors from each pair eventually reveals the common binomial factor, leading to the expression being factored completely.

AC Method

The AC Method is a technique used for factoring quadratic trinomials, especially when the coefficient of the quadratic term is not 1. This method involves multiplying the coefficient 'a' with the constant term 'c' to find two numbers that multiply to ac and add to the middle coefficient 'b'. Once these numbers are found, the middle term is split accordingly, facilitating further factoring.

Quadratic Trinomial

A quadratic trinomial is a second-degree polynomial that consists of three terms, typically written in the form ax² + bx + c. Understanding this form is essential because factoring such expressions helps in finding the roots of quadratic equations and in simplifying algebraic expressions across various mathematical problems.

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