Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Problem 6

Factorise \(3 x^{3}+17 x^{2}+11 x\)

Short Answer

Expert verified
Answer: The factorization of the polynomial expression \(3x^3 + 17x^2 + 11x\) is \(x(3x^2 + 17x + 11)\).

Step by step solution

01

Identify the GCF

First, we need to find the greatest common factor of the coefficients and the variable terms. In this case, the GCF of the coefficients (3, 17, and 11) is 1, and the GCF of the variable terms (\(x^3\), \(x^2\), and \(x\)) is \(x\). So, the overall GCF is \(1x\).
02

Factor out the GCF

Next, we will factor out the GCF (\(1x\)) from each term in the given expression. \(3x^3 + 17x^2 + 11x = x(3x^2 + 17x + 11)\)
03

Factor the quadratic expression

Now, we need to factorise the quadratic expression inside the parenthesis (\(3x^2 + 17x + 11\)). To do this, we need to find two binomials whose product gives the quadratic expression. In this case, there are no such binomials as the expression is prime. Thus, we have reached the final factorisation.
04

Write the final factorization

Since we were not able to factorise the quadratic expression further, we can now write the final factorisation of the given expression: \(3x^3 + 17x^2 + 11x = x(3x^2 + 17x + 11)\)

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Without using a calculator find the value of $$ 3 \frac{13}{17}+\frac{4-\frac{1}{3}}{3 / 7} $$

Remove the brackets from the given expression: \((x-1)(x+2)\)

In each case, simplify the given expression, if possible. \( x^{2}+3 x+1\)

Transpose each of the following formulae to make the given variable the subject: (a) \(x=\frac{c}{y}\), for \(y\) (b) \(x=\frac{c}{y}\), for \(c\) (c) \(k=\frac{2 n+5}{n+3}\), for \(n\) (d) \(T=2 \pi \sqrt{\frac{R-L}{g}}\), for \(R\)

Remove the brackets from the given expression: \((x+2)(x-2)\)
See all solutions

Recommended explanations on Physics Textbooks

Famous Physicists

Read Explanation

Work Energy and Power

Read Explanation

Solid State Physics

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation

Wave Optics

Read Explanation

Geometrical and Physical Optics

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.

Sign-up for free