Question

Factor the polynomial in part (a). Then use substitution to help factor the polynomials in parts (b) and (c). a. $u^{2}-10 u+25$ b. $x^{4}-10 x^{2}+25$ c. $(a+1)^{2}-10(a+1)+25$

Name: Problem 67, Chapter 4: Intermediate Algebra
Uploaded: 2020-07-03T09:16:18-08:00
Duration: 1 min 22 s
Channel: Ankit Gupta
Description: Factor the polynomial in part (a). Then use substitution to help factor the polynomials in parts (b) and (c). a. u^2-10 u+25 b. x^4-10 x^2+25 c. (a+1)^2-10(a+1)+25

   Factor the polynomial in part (a). Then use substitution to help factor the polynomials in parts (b) and (c).
a. $u^{2}-10 u+25$
b. $x^{4}-10 x^{2}+25$
c. $(a+1)^{2}-10(a+1)+25$

Intermediate Algebra

Julie Miller, Molly… 5th Edition

Chapter 4, Problem 67

Instant Answer

Solved by Expert Ankit Gupta

07/03/2020

Step 1

This is a perfect square trinomial, which can be factored as $(u-5)^{2}$. Show more…

Show all steps

Thanks for your feedback!

Factor the polynomial in part (a). Then use substitution to help factor the polynomials in parts (b) and (c). a. $u^{2}-10 u+25$ b. $x^{4}-10 x^{2}+25$ c. $(a+1)^{2}-10(a+1)+25$

Play audio

Feedback

Ankit Gupta and 98 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Polynomial Factorization

This is the process of expressing a polynomial as a product of simpler polynomials. Factoring is a fundamental algebraic technique used to simplify expressions, solve equations, and reveal properties of a polynomial by writing it as a product of its factors.

Perfect Square Trinomial

A perfect square trinomial is a specific type of polynomial that can be written as the square of a binomial. This structure typically takes the form a² ± 2ab + b², and recognizing this pattern can simplify both the factoring process and the solving of polynomial equations.

Substitution Method

The substitution method involves replacing a complex expression within a polynomial with a single variable to simplify the structure. This technique is particularly useful when dealing with polynomials that exhibit a repeated structure or pattern, enabling easier factoring and manipulation.

Please give Ace some feedback