Question

Factor each trinomial completely. $$ 16 n^{2}+14 n+3 $$

   Factor each trinomial completely.
$$ 16 n^{2}+14 n+3 $$

Prealgebra & Introductory Algebra

Prealgebra & Introductory Algebra

Julie Miller, Molly… 2nd Edition

Chapter 13, Problem 62

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Solved by Expert Victor Salazar

04/05/2022

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Factor each trinomial completely. $$ 16 n^{2}+14 n+3 $$

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Key Concepts

Quadratic Trinomials

A quadratic trinomial is a polynomial with three terms, usually written in the form ax² + bx + c. Factoring these expressions involves finding two binomials whose product is the given quadratic, a foundational skill in algebra that aids in solving quadratic equations and understanding their properties.

The AC Method

The AC method is a systematic approach to factoring quadratic trinomials, especially when the leading coefficient is not 1. It involves multiplying the coefficient of x² (a) by the constant term (c) to find a product and then identifying two factors of this product that add up to the coefficient of x (b). These factors are used to split the middle term, simplifying the expression into groups that can be factored further.

Factoring by Grouping

Factoring by grouping is a technique used after splitting the middle term in a quadratic trinomial. This method involves organizing the four-term expression into two pairs, factoring out common factors from each pair, and then factoring the common binomial factor. It is an essential strategy for breaking down more complicated polynomials into simpler, solvable parts.

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