Answered

From beginner to expert, IDNLearn.com has answers for everyone. Whether it's a simple query or a complex problem, our experts have the answers you need.

What is the difference of the polynomials?

[tex]\[ \left(x^4 + x^3 + x^2 + x\right) - \left(x^4 - x^3 + x^2 - x\right) \][/tex]

A. [tex]\( 2x^2 \)[/tex]
B. [tex]\( 2x^3 + 2x \)[/tex]
C. [tex]\( x^6 + x^2 \)[/tex]
D. [tex]\( 2x^6 + 2x^2 \)[/tex]

Sagot :

GinnyAnsweridn
To find the difference between two given polynomials [tex]\( P(x) \)[/tex] and [tex]\( Q(x) \)[/tex], follow these steps:

First, identify the polynomials:
[tex]\[ P(x) = x^4 + x^3 + x^2 + x \][/tex]
[tex]\[ Q(x) = x^4 - x^3 + x^2 - x \][/tex]

Next, subtract [tex]\( Q(x) \)[/tex] from [tex]\( P(x) \)[/tex]:
[tex]\[ P(x) - Q(x) = (x^4 + x^3 + x^2 + x) - (x^4 - x^3 + x^2 - x) \][/tex]

Distribute the negative sign across the terms of [tex]\( Q(x) \)[/tex]:
[tex]\[ P(x) - Q(x) = x^4 + x^3 + x^2 + x - x^4 + x^3 - x^2 + x \][/tex]

Combine like terms:
[tex]\[ P(x) - Q(x) = (x^4 - x^4) + (x^3 + x^3) + (x^2 - x^2) + (x + x) \][/tex]

Simplify each set of like terms:
[tex]\[ P(x) - Q(x) = 0 + 2x^3 + 0 + 2x \][/tex]

So, the difference of the polynomials is:
[tex]\[ 2x^3 + 2x \][/tex]

Therefore, the correct answer is:
[tex]\[ 2x^3 + 2x \][/tex]
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Find the answers you need at IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.