Question

Subtract the polynomial expressions and simplify completely. (3x5+7x2−4x+8)−(4x4+8x2−3x+7)

Answer 1

To subtract the polynomial expressions \((3x^5 + 7x^2 - 4x + 8) - (4x^4 + 8x^2 - 3x + 7)\), we first distribute the negative sign across the second polynomial:

\[
3x^5 + 7x^2 - 4x + 8 - 4x^4 - 8x^2 + 3x - 7
\]

Next, we can combine like terms. We will align the terms according to their degrees:

1. The \(x^5\) term: \(3x^5\)
2. The \(x^4\) term: \(-4x^4\)
3. The \(x^2\) terms: \(7x^2 - 8x^2 = -1x^2\) (or \(-x^2\))
4. The \(x\) terms: \(-4x + 3x = -1x\) (or \(-x\))
5. The constant terms: \(8 - 7 = 1\)

Putting it all together, we have:

\[
3x^5 - 4x^4 - x^2 - x + 1
\]

Thus, the simplified result of the polynomial subtraction is:

\[
\boxed{3x^5 - 4x^4 - x^2 - x + 1}
\]