/*! 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 3 Factor each trinomial, or state ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 3

Factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$x^{2}+7 x+10$$

Short Answer

Expert verified
The trinomial \(x^{2}+7 x+10\) factors into \((x+5)(x+2)\).

Step by step solution

01

Identify the Factors

To begin with, identify two numbers that multiply to 10 (from the constant term) and add up to 7 (from the coefficient of \(x\)). The numbers that meet this condition are 5 and 2, because \(5*2 = 10\) and \(5 + 2 = 7\).
02

Apply the Binomial Formula

This gives us a binomial factorisation of the trinomial. Substitute these values into the binomial formula \((x+a)(x+b)\), where \(a\) and \(b\) are the two numbers found in the previous step: \(a=5, b=2 \) to get \((x+5)(x+2)\).
03

Check the Factorization

Use the FOIL method to expand the factors and verify the original trinomial. FOIL stands for First terms, Outer terms, Inner terms, and Last terms multiplication. So, applying FOIL on \( (x+5)(x+2)\): First = \(x*x\), Outer = \(x*2\), Inner = \(5*x\), Last = \(5*2\) which results in \(x^{2}+7 x+10\). This matches the original trinomial, hence the factorization is correct.

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

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

Factor completely. $$x^{2}+8 x+16-25 a^{2}$$

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. $$9 y^{2}+64$$

Factor completely. $$(x-6)^{2}-9 a^{2}$$

Contain polynomials in several variables. Factor each polynomial completely and check using multiplication. $$3 x^{4}-9 x^{3} y+3 x^{2} y^{2}$$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

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.