How do you divide #(2x^4-20x^2+5x+3)÷(x-3)#?

Question

Avery Alexander · Accepted Answer

#2x^3+6x^2-2x-1#

Use a process called "synthetic division" which is simply an extended version of long division:

Ethan Adkins · Answer

undefined To divide (2x^4-20x^2+5x+3) by (x-3), you can use long division. Here are the steps:

1. Divide the first term of the dividend (2x^4) by the first term of the divisor (x). The result is 2x^3.
2. Multiply the divisor (x-3) by the quotient obtained in step 1 (2x^3). The result is 2x^4-6x^3.
3. Subtract the result obtained in step 2 from the dividend (2x^4-20x^2+5x+3). This gives you -6x^3-20x^2+5x+3.
4. Bring down the next term from the dividend, which is 5x.
5. Divide the first term of the new dividend (-6x^3) by the first term of the divisor (x). The result is -6x^2.
6. Multiply the divisor (x-3) by the quotient obtained in step 5 (-6x^2). The result is -6x^3+18x^2.
7. Subtract the result obtained in step 6 from the new dividend (-6x^3-20x^2+5x+3). This gives you -38x^2+5x+3.
8. Bring down the next term from the dividend, which is 3.
9. Divide the first term of the new dividend (-38x^2) by the first term of the divisor (x). The result is -38x.
10. Multiply the divisor (x-3) by the quotient obtained in step 9 (-38x). The result is -38x^2+114x.
11. Subtract the result obtained in step 10 from the new dividend (-38x^2+5x+3). This gives you 109x+3.
12. Bring down the next term from the dividend, which is 3.
13. Divide the first term of the new dividend (109x) by the first term of the divisor (x). The result is 109.
14. Multiply the divisor (x-3) by the quotient obtained in step 13 (109). The result is 109x-327.
15. Subtract the result obtained in step 14 from the new dividend (109x+3). This gives you 330.
16. There are no more terms to bring down, and the remainder is 330.
17. The quotient is 2x^3-6x^2-38x+109, and the remainder is 330.

Therefore, (2x^4-20x^2+5x+3) divided by (x-3) equals 2x^3-6x^2-38x+109 with a remainder of 330.

Jameson Allen · Answer

undefined You can use polynomial long division or synthetic division to divide (2x^4 - 20x^2 + 5x + 3) by (x - 3). Here's the process using polynomial long division:

1. Divide the first term of the dividend by the first term of the divisor: (2x^4 ÷ x) = 2x^3.
2. Multiply the divisor (x - 3) by the quotient term (2x^3) and subtract the result from the dividend.
3. Bring down the next term of the dividend and repeat the process until there are no more terms left to bring down or the degree of the remainder is less than the degree of the divisor.

Continuing this process, you'll eventually find the quotient and remainder.