Question
upstudy study bank question image url

)) Factor \( x^{4}+14 x^{2}+49 \) completely. All factors in your answer should have integer coefficients. Sideo

Ask by Cox Christensen. in the United States
Mar 12,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

\( x^{4}+14x^{2}+49 = (x^{2}+7)^{2} \)

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

Bonus Knowledge

To factor \( x^{4}+14 x^{2}+49 \) completely, we can start by recognizing that the expression can be treated as a quadratic in terms of \( x^2 \). Let's set \( y = x^2 \), transforming the expression into \( y^2 + 14y + 49 \). This can be factored as \( (y + 7)(y + 7) \) or \( (y + 7)^2 \). Substituting back \( y = x^2 \) gives us \( (x^2 + 7)^2 \). Thus, the complete factorization of the original polynomial is: \[ (x^2 + 7)^2 \] And there you have it—factor the quadratic first to reveal its perfect square nature! For a deeper understanding, remember that recognizing patterns can simplify your factoring journey. Always look for perfect squares or sum of squares. Moreover, ensure to check the degree of polynomials when applying these techniques; minor miscalculations can lead to frustrating dead ends! So, keep your factoring skills sharp—being familiar with common structures can significantly speed up your work.

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