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The image you've uploaded involves mathematical content related to polynomial long division and synthetic division, used to divide one polynomial by another. The division problems are part of solving polynomial equations or simplifying expressions in algebra.

From the visible text, it appears the task involves dividing the polynomial \( f(x) = 4x^4 + 8x^3 - 15x^2 + 4x - 900 \) by \( x^2 + 5 \) using polynomial long division, which is a step towards determining how many items (such as pairs of pants, in a practical example) can be made given a function describing material usage.

The division should provide a quotient and a remainder, the latter indicating any leftover material or quantity that does not completely fit into the division pattern.

### Solving the Polynomial Division:

Let's perform the division of \( 4x^4 + 8x^3 - 15x^2 + 4x - 900 \) by \( x^2 + 5 \) to find the quotient and remainder.

Shall we proceed with this calculation?

Divide the polynomial f(x) = 4x^4 + 8x^3 - 15x^2 + 4x - 900 by (x^2 + 5) to determine how many items (such as pairs of pants) can be made, and find the remainder for the leftover material. Perform the calculation using polynomial long division.

Explore how to divide the polynomial f(x) = 4x^4 + 8x^3 - 15x^2 + 4x - 900 by (x^2 + 5) using polynomial long division. This step-by-step explanation covers algebraic concepts and helps determine the quotient and remainder, essential for practical applications like material calculations.

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