/*! 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] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 17

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

Short Answer

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

Step by step solution

01

Identify the coefficients and constant

The given trinomial is \(x^{2}+5x+6\). Here, the coefficient of \(x^{2}\) is 1, the coefficient of \(x\) is 5 and the constant is 6.
02

Find the pair of numbers

We need to find two numbers that multiply to give 6 (the product of the coefficient of \(x^{2}\) and the constant) and add to 5 (the coefficient of \(x\)). After some trials, we see that these two numbers are 2 and 3, because 2*3 = 6 and 2+3 = 5.
03

Write the factors

The trinomial can be rewritten as \(x^{2}+2x+3x+6\). By grouping the first two and the last two terms together we get \(x(x+2)+3(x+2)\). The trinomial gets factored as \((x+2)(x+3)\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

$$\text { Factor completely.}$$ $$3 x^{2}+5 x y^{2}+2 y^{4}$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$4^{-2}<4^{-3}$$

Determine whether each statement in Exercises 43鈥�50 is true or false. $$4 \geq-7$$

$$\text { Factor completely.}$$ $$y^{7}+y$$

$$\text { Factor completely.}$$ $$7 x^{4}+34 x^{2}-5$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.