Question

1. (3w³ + 7w² - 4w + 3) ÷ (w + 3)

Explanation:

Step 1: Use Polynomial Long Division

We divide the polynomial \(3w^{3}+7w^{2}-4w + 3\) by \(w + 3\).

First, divide the leading term of the dividend \(3w^{3}\) by the leading term of the divisor \(w\), we get \(3w^{2}\).
Multiply the divisor \(w + 3\) by \(3w^{2}\): \(3w^{2}(w + 3)=3w^{3}+9w^{2}\)
Subtract this from the dividend: \((3w^{3}+7w^{2}-4w + 3)-(3w^{3}+9w^{2})=- 2w^{2}-4w + 3\)

Step 2: Continue the Division

Now, divide the leading term of \(-2w^{2}\) by \(w\), we get \(-2w\).
Multiply the divisor \(w + 3\) by \(-2w\): \(-2w(w + 3)=-2w^{2}-6w\)
Subtract this from \(-2w^{2}-4w + 3\): \((-2w^{2}-4w + 3)-(-2w^{2}-6w)=2w + 3\)

Step 3: Continue the Division

Divide the leading term of \(2w\) by \(w\), we get \(2\).
Multiply the divisor \(w + 3\) by \(2\): \(2(w + 3)=2w+6\)
Subtract this from \(2w + 3\): \((2w + 3)-(2w + 6)=-3\)

So, \(\frac{3w^{3}+7w^{2}-4w + 3}{w + 3}=3w^{2}-2w + 2-\frac{3}{w + 3}\)

Answer:

\(3w^{2}-2w + 2-\frac{3}{w + 3}\)