Question

what is the difference of the polynomials?

\\((x^4 + x^3 + x^2 + x) - (x^4 - x^3 + x^2 - x)\\)

• \\(2x^2\\)
• \\(2x^3 + 2x\\)
• \\(x^6 + x^2\\)
• \\(2x^6 + 2x^2\\)

Explanation:

⚡ Using what you learned: adding and subtracting polynomials

Step 1: Distribute the negative sign

$$ (x^4 + x^3 + x^2 + x) - (x^4 - x^3 + x^2 - x) = x^4 + x^3 + x^2 + x - x^4 + x^3 - x^2 + x $$

Step 2: Combine like terms

$$ (x^4 - x^4) + (x^3 + x^3) + (x^2 - x^2) + (x + x) = 2x^3 + 2x $$

Answer:

\(2x^3 + 2x\)