# How do you divide #( -x^4 + 3x^3 + 9x^2 +4x)/(2x^2-3x)#?

Trigonometry long division gives quotient of

By signing up, you agree to our Terms of Service and Privacy Policy

To divide (-x^4 + 3x^3 + 9x^2 + 4x) by (2x^2 - 3x), we can use polynomial long division.

First, we divide the highest degree term of the numerator by the highest degree term of the denominator. In this case, (-x^4) ÷ (2x^2) gives us -0.5x^2.

Next, we multiply the entire denominator (2x^2 - 3x) by the result we obtained (-0.5x^2), giving us (-x^4 + 1.5x^3).

We subtract this result from the numerator (-x^4 + 3x^3 + 9x^2 + 4x) to get (4.5x^3 + 9x^2 + 4x).

We repeat the process by dividing the highest degree term of the new numerator (4.5x^3) by the highest degree term of the denominator (2x^2), which gives us 2.25x.

We multiply the entire denominator (2x^2 - 3x) by the result we obtained (2.25x), giving us (4.5x^3 - 6.75x^2).

We subtract this result from the new numerator (4.5x^3 + 9x^2 + 4x) to get (15.75x^2 + 4x).

We continue this process until we have no more terms to divide. In this case, we divide (15.75x^2 + 4x) by (2x^2 - 3x).

The final result of the division is (-0.5x^2 + 2.25x + 7.875) with a remainder of (4x + 7.875).

By signing up, you agree to our Terms of Service and Privacy Policy

To divide ( \frac{-x^4 + 3x^3 + 9x^2 + 4x}{2x^2 - 3x} ), we perform polynomial long division or synthetic division. Let's use polynomial long division in this case.

Step 1: Divide the leading term of the numerator by the leading term of the denominator. This gives us the first term of the quotient. In this case, ( \frac{-x^4}{2x^2} = -\frac{1}{2}x^2 ).

Step 2: Multiply the entire denominator by the first term of the quotient and subtract the result from the numerator. This gives us the remainder after dividing by the leading term.

Step 3: Repeat the process with the new polynomial obtained in the previous step.

Performing these steps iteratively, we can find the quotient and the remainder. Once we have the quotient, we can write the division as:

[ \frac{-x^4 + 3x^3 + 9x^2 + 4x}{2x^2 - 3x} = -\frac{1}{2}x^2 + \frac{3}{4}x + \frac{33}{8} + \frac{4}{8x - 6} ]

This is the quotient, and ( \frac{4}{8x - 6} ) is the remainder.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7