/*! 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 35 Factor each trinomial, or state ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 35

Factor each trinomial, or state that the trinomial is prime. $$2 x^{2}+3 x y+y^{2}$$

Short Answer

Expert verified
The trinomial \(2x^{2} + 3xy + y^{2}\) is prime.

Step by step solution

01

Identify the form

Identify if the trinomial is in the form \(a^{2} + 2ab + b^{2}\). In this case, \(a^{2} = 2x^{2}\) where \(a = 鈭�2x\), \(2ab = 3xy\) and \(b^{2} = y^{2}\) where \(b = y\). Thus, \(a = 鈭�2x\), \(b = y\) and \(2ab = 2*鈭�2x*y\). However, our \(2ab\) isn't matching with the one in the problem which is \(3xy\). Hence, this trinomial is not in the form of \(a^{2} + 2ab + b^{2}\).
02

Factor the trinomial

Since the trinomial is not in the form of a perfect square trinomial, we then try to factor it. Here, there are no common factors among \(2x^{2} + 3xy + y^{2}\), and it doesn't factor as a product of binomials because there are no pair of numbers that multiplies to \(2\) (the coefficient of \(x^{2}\)) and also adds to \(3\) (the coefficient of \(xy\)).
03

State that the trinomial is prime

After observing that the trinomial fits neither the perfect square trinomial format nor can it be factored as a product of binomials, we can conclude that this trinomial is prime, meaning it can't be factored further.

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

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. A company manufactures and sells blank audiocassette tapes. The weekly fixed cost is \(\$ 10,000\) and it costs \(\$ 0.40\) to produce each tape. The selling price is \(\$ 2.00\) per tape. How many tapes must be produced and sold each week for the company to generate a profit?

Perform the indicated operations. Simplify the result, if possible. $$\frac{y^{-1}-(y+2)^{-1}}{2}$$

Explain how to multiply rational expressions.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When performing the division $$\frac{7 x}{x+3}+\frac{(x+3)^{2}}{x-5}$$ I began by dividing the numerator and the denominator by the common factor, \(x+3\).

Perform the indicated operations. Simplify the result, if possible. $$\left(4-\frac{3}{x+2}\right)\left(1+\frac{5}{x-1}\right)$$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

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.