Question
upstudy study bank question image url

a) Divide \( x+2 x^{2}+3 x+4 \) by \( x+2 \) b) Divide \( 2 x^{3}-x^{2}+3 x-2 \) by \( x+3 \) c) Divide \( a^{3}+64 b^{3} \) by \( a+4 b \) 2. Find the remainder when \( x^{3}+3 x^{2}-x+7 \) is divided by \( 3 x-1 \).

Ask by Cervantes Mullins. in South Africa
Mar 11,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

**(a) Divide \( x + 2x^{2} + 3x + 4 \) by \( x + 2 \):** Quotient: \( 2x \) Remainder: \( 4 \) **(b) Divide \( 2x^{3} - x^{2} + 3x - 2 \) by \( x + 3 \):** Quotient: \( 2x^{2} - 7x + 24 \) Remainder: \(-74\) **(c) Divide \( a^{3} + 64b^{3} \) by \( a + 4b \):** Quotient: \( a^{2} - 4ab + 16b^{2} \) Remainder: \( 0 \) **(2) Remainder when \( x^{3} + 3x^{2} - x + 7 \) is divided by \( 3x - 1 \):** Remainder: \( \frac{190}{27} \)

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

The Deep Dive

When dividing polynomials, it’s not just about the numbers; it’s also about the fun process of synthetic or long division! For part a), when you divide \( x + 2x^2 + 3x + 4 \) by \( x + 2 \), you're essentially arranging the terms in descending order, which is like sorting your toys! After simplification, you find the quotient is \( 2x + 3 \) with a remainder of \( 0 \). For part d), the Remainder Theorem comes to the rescue! To find the remainder when dividing \( x^3 + 3x^2 - x + 7 \) by \( 3x - 1 \), you can evaluate the polynomial at \( x = \frac{1}{3} \). Plugging this into the polynomial gives you the remainder, which makes this method not only efficient but a bit like a magic trick in math!

Latest Algebra Questions

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy