/*! 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 112 What is a perfect square trinomi... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 112

What is a perfect square trinomial and how is it factored?

Short Answer

Expert verified
A perfect square trinomial is a polynomial of the form \(a^2 + 2ab + b^2\) or \(a^2 - 2ab + b^2\). It can be factored as \((a+b)^2\) or \((a-b)^2\), respectively. For example, the trinomial \(x^2 + 6x + 9\) can be factored as \((x+3)^2\).

Step by step solution

01

Identify the Perfect Square Trinomial

A perfect square trinomial is a polynomial of the form \(a^2 + 2ab + b^2\) or \(a^2 - 2ab + b^2\). This form should be able to be written as \((a+b)^2\) or \((a-b)^2\) respectively.
02

Understanding Factoring a Perfect Square Trinomial

Factoring a perfect square trinomial involves expressing the trinomial in one of the forms mentioned previously. Essentially, you are looking for values of \(a\) and \(b\) such that the trinomial fits the pattern of either \(a^2 + 2ab + b^2\) or \(a^2 - 2ab + b^2\). The trinomial can be factored as \((a+b)^2\) or \((a-b)^2\), respectively.
03

Example of Factoring a Perfect Square Trinomial

For example, let's factor \(x^2 + 6x + 9\). We can see that the trinomial follows the pattern \(a^2 + 2ab + b^2\). By comparing each term in the trinomial to the pattern, we can see that \(a=x\) and \(b=3\), therefore the trinomial can be factored as \((x+3)^2\).

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

Factor: \(9 x^{2}-16 .\)

Now let's move on to factorizations that may require two or more techniques. Factor completely, or state that the polynomial is prime. Check factorizations using multiplication or a graphing utility. $$-4 y^{3}+28 y^{2}-40 y$$

Now let's move on to factorizations that may require two or more techniques. Factor completely, or state that the polynomial is prime. Check factorizations using multiplication or a graphing utility. $$-7 y^{3}+21 y^{2}-14 y$$

Contain polynomials in several variables. Factor each polynomial completely and check using multiplication. $$24 a^{4} b+60 a^{3} b^{2}+150 a^{2} b^{3}$$

Use the \([\mathrm{GRAPH}]\) or \([\mathrm { TABLE }]\) feature of a graphing utility to determine if the polynomial on the left side of each equation has been correctly factored. If not, factor the polynomial correctly and then use your graphing utility to verify the factorization. $$4 x^{2}-12 x+9=(4 x-3)^{2} ;[-5,5,1] \text { by }[0,20,1]$$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Statistics

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.