How do you divide #(5x^4+2x^3-9x+12)/(x^2-3x+4)#?

Question

Isaiah Anthony · Accepted Answer

#-149x + 372 + (5x^2 + 17 - 30)/(x^2 - 3x +4)#

you have to do long division,

Here is my best attempt at the answer and I hope it's right, because I worked for a very long time to draw it out on paint. If it is not correct, I am sure the setup is correct, so you can use it to repeat the calculation for new problems.

Hazel Anglin · Answer

undefined To divide (5x^4+2x^3-9x+12) by (x^2-3x+4), you can use long division or synthetic division. Here is the step-by-step process using long division:

1. Divide the first term of the numerator (5x^4) by the first term of the denominator (x^2). The result is 5x^2.
2. Multiply the entire denominator (x^2-3x+4) by the result from step 1 (5x^2), and subtract it from the numerator (5x^4+2x^3-9x+12).
   This gives you (5x^4+2x^3-9x+12) - (5x^2 * (x^2-3x+4)).
   Simplifying further, you get 2x^3-9x+12 - (5x^4-15x^3+20x^2).
3. Bring down the next term from the numerator, which is -15x^3.
4. Divide the first term of the new expression (-15x^3) by the first term of the denominator (x^2). The result is -15x.
5. Multiply the entire denominator (x^2-3x+4) by the result from step 4 (-15x), and subtract it from the new expression.
   This gives you -15x^3 + 2x^3 - 9x + 12 - (-15x * (x^2-3x+4)).
   Simplifying further, you get -15x^3 + 2x^3 - 9x + 12 - (-15x^3 + 45x^2 - 60x).
6. Continue this process until you have divided all the terms. The final result will be the quotient.

The quotient of (5x^4+2x^3-9x+12)/(x^2-3x+4) is 5x^2 - 15x + 3, with a remainder of (-60x + 12)/(x^2-3x+4).