# How do you divide #( -3x^3+ 4x^2 + 12x + 9 )/(x - 2 )#?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Checked in Maple:

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

To divide (-3x^3 + 4x^2 + 12x + 9) by (x - 2), you can use long division or synthetic division. Here is the step-by-step process using long division:

- Divide the first term of the dividend (-3x^3) by the first term of the divisor (x). This gives you -3x^2.
- Multiply the divisor (x - 2) by the quotient obtained in step 1 (-3x^2). This gives you (-3x^2)(x - 2) = -3x^3 + 6x^2.
- Subtract the result obtained in step 2 from the original dividend (-3x^3 + 4x^2 + 12x + 9) to get the new dividend: (4x^2 + 12x + 9) - (-3x^3 + 6x^2) = -3x^3 + 4x^2 + 12x + 9 + 3x^3 - 6x^2 = 10x^2 + 12x + 9.
- Repeat steps 1-3 with the new dividend (10x^2 + 12x + 9) until the degree of the new dividend is less than the degree of the divisor.

Continuing the process: 5. Divide the first term of the new dividend (10x^2) by the first term of the divisor (x). This gives you 10x. 6. Multiply the divisor (x - 2) by the quotient obtained in step 5 (10x). This gives you (10x)(x - 2) = 10x^2 - 20x. 7. Subtract the result obtained in step 6 from the new dividend (10x^2 + 12x + 9) to get the new dividend: (12x + 9) - (10x^2 - 20x) = 10x^2 - 20x + 12x + 9 = 10x^2 - 8x + 9. 8. Repeat steps 5-7 with the new dividend (10x^2 - 8x + 9) until the degree of the new dividend is less than the degree of the divisor.

Continuing the process: 9. Divide the first term of the new dividend (10x^2) by the first term of the divisor (x). This gives you 10x. 10. Multiply the divisor (x - 2) by the quotient obtained in step 9 (10x). This gives you (10x)(x - 2) = 10x^2 - 20x. 11. Subtract the result obtained in step 10 from the new dividend (10x^2 - 8x + 9) to get the remainder: (-8x + 9) - (10x^2 - 20x) = -10x^2 + 12x + 9.

Therefore, the quotient is -3x^2 + 10x + 10, and the remainder is -10x^2 + 12x + 9.

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