x^4+5x3
_______
3x^2
How would I do this? I can't seem to figure out how to set this problem up. The x^4 is confusing me greatly.
factor out x^3
x^3(x+5)/3x^2=x(x+5)/3
Is this division?
see now im more confused because I don't see how I can factor out x^3
yeah it division
To divide the polynomial x^4 + 5x^3 by 3x^2, you can use long division. Here's how to set up the problem:
1. Start by writing the dividend (x^4 + 5x^3) inside the long division bracket.
2. Divide the first term of the dividend (x^4) by the divisor (3x^2). The result is (x^4)/(3x^2) = (1/3)x^2.
3. Write this result above the long division bracket, above the term with the highest degree (x^4).
4. Multiply the divisor (3x^2) by the result you obtained in step 2, which is (1/3)x^2. The product is (1/3)x^2 * 3x^2 = (1/3) * 3 * x^2 * x^2 = x^4.
5. Subtract the product from the polynomial inside the long division bracket. This means subtracting x^4 from x^4 + 5x^3, leaving you with 5x^3.
6. Bring down the next term from the dividend, which is 0x^2. Write this below the subtraction line, next to the 5x^3.
7. Repeat steps 2-6 with the new polynomial (5x^3 + 0x^2) and the divisor (3x^2). Divide the first term (5x^3) by the divisor (3x^2) and write the result above the long division bracket.
8. Multiply the divisor (3x^2) by the result obtained in step 7 and subtract the product from the polynomial inside the long division bracket. This will give you a new polynomial to continue the process.
9. Repeat steps 2-8 until you have finished dividing all the terms of the polynomial.
Following these steps will allow you to divide x^4 + 5x^3 by 3x^2 and obtain the quotient.