Question

Factor the trinomial. $x^{2}-8 x+12$

   Factor the trinomial.
$x^{2}-8 x+12$

Algebra and Trigonometry

Algebra and Trigonometry

Judith A. Beecher,… 4th Edition

Chapter 0, Problem 22

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Solved by Expert Ankit Gupta

07/20/2020

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Those numbers are -6 and -2. Show more…

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Factor the trinomial. $x^{2}-8 x+12$

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Key Concepts

Sum-Product Method

The sum-product method is a strategic approach used in factoring quadratic trinomials. This method focuses on identifying two numbers that have a product equal to c (the constant term) and a sum equal to b (the coefficient of the linear term). Once these numbers are determined, they are used to split the middle term, facilitating the factorization process.

Factoring Quadratic Trinomials

Factoring quadratic trinomials involves rewriting the quadratic expression as the product of two binomials. This process is based on finding two numbers that multiply to give the constant term c, while also summing to the coefficient b. Recognizing these relationships allows for the quadratic to be expressed in a factored form.

Quadratic Expression

A quadratic expression is a second-degree polynomial, typically written in the standard form ax² + bx + c, where a, b, and c are constants and a is not zero. Understanding this form is crucial as it lays the groundwork for applying various algebraic techniques, including factoring.

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