Factor each trinomial completely. See Examples 1–7. ( Hint: In Exercises 55–58, first write the

step 1 Whenever we're going to factor, we do want to start by looking for a greatest common factor. The

Factor each trinomial completely. See Examples 1

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Key Concepts

Substitution Method

This technique involves replacing a repeated subexpression (such as x²) with a new variable (commonly u) to transform a higher-degree polynomial into a quadratic form, making the factoring process more straightforward.

Quadratic Factoring

Once the expression is rewritten as a quadratic (for example, 24u² + 55u - 24), factoring methods for quadratics, such as finding two numbers that multiply to the product of the leading coefficient and the constant term and add to the middle coefficient, can be employed.

Descending Order of Polynomial

Arranging the terms of a polynomial in descending order of degree (from highest to lowest power) is essential for clarity and proper application of standard factoring techniques.

AC Method

This method involves multiplying the coefficient of the leading term by the constant term and then finding two numbers that add to the middle term’s coefficient, which is a systematic approach used for factoring trinomials effectively.

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