/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 17 Factor each trinomial, or state ... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Factor each trinomial, or state that the trinomial is prime. $$x^{2}+5 x+6$$

Short Answer

Expert verified
So, the factored form of the trinomial \(x^{2}+5x+6\) is \( (x+2)(x+3)\).

Step by step solution

01

Identify the structure

Recognize that the given expression is a quadratic trinomial in the form \(ax^2 + bx + c\), where \(a=1\), \(b=5\), and \(c=6\).
02

Find factors

Search for two numbers that multiply to 6 (the value of \(c\)) and add up to 5 (the value of \(b\)). The numbers 2 and 3 fit these criteria because \(2*3 = 6\) and \(2+3 = 5\).
03

Write the factors

Write the trinomial as a product of two binomials using the identified numbers as the coefficients of \(x\) in the binomials, giving \( (x+2)(x+3) \).

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