Question

What is the quotient of the following? 35x^5−20x^4+45x^3 divided by 5x^2 (1 point)

Answer 1

To divide the polynomial \( 35x^5 - 20x^4 + 45x^3 \) by \( 5x^2 \), we can divide each term of the polynomial by \( 5x^2 \).

1. Divide \( 35x^5 \) by \( 5x^2 \):
\[
\frac{35x^5}{5x^2} = 7x^{5-2} = 7x^3
\]

2. Divide \( -20x^4 \) by \( 5x^2 \):
\[
\frac{-20x^4}{5x^2} = -4x^{4-2} = -4x^2
\]

3. Divide \( 45x^3 \) by \( 5x^2 \):
\[
\frac{45x^3}{5x^2} = 9x^{3-2} = 9x
\]

Now, we can combine these results:
\[
\frac{35x^5 - 20x^4 + 45x^3}{5x^2} = 7x^3 - 4x^2 + 9x
\]

So, the final quotient is:
\[
\boxed{7x^3 - 4x^2 + 9x}
\]