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

Question

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

Julia Adams · Accepted Answer

#y=((x^2+3)(4x-5)(3x-1))/(2x-3)# #y=(4x^3-5x^2+9x-3)/(2x-3)# Divide #2# terms at once by a common factor. #y=(x^2(4x-5)+3(3x-1))/(2x-3)# Rewrite the equation. #y=((x^2+3)(4x-5)(3x-1))/(2x-3)#, #x!=3/2# Since the equation cannot be simplified any further, the final answer is #y=((x^2+3)(4x-5)(3x-1))/(2x-3)# where #x!=3/2#.

Isaiah Anthony · Answer

undefined To divide (4x^3-5x^2+9x-3) by (2x-3), you can use long division. Here are the steps:

1. Divide the first term of the numerator (4x^3) by the first term of the denominator (2x). This gives you 2x^2.
2. Multiply the entire denominator (2x-3) by the result from step 1 (2x^2), and subtract it from the numerator (4x^3-5x^2+9x-3).
   This gives you (4x^3-5x^2+9x-3) - (2x^2 * (2x-3)).
   Simplifying this expression gives you (4x^3-5x^2+9x-3) - (4x^3-6x^2).
   Combining like terms gives you -x^2+9x-3.
3. Bring down the next term from the numerator, which is 0x^2. Now you have (-x^2+9x-3).
4. Divide the first term of the new expression (-x^2) by the first term of the denominator (2x). This gives you -0.5x.
5. Multiply the entire denominator (2x-3) by the result from step 4 (-0.5x), and subtract it from the new expression (-x^2+9x-3).
   This gives you (-x^2+9x-3) - (-0.5x * (2x-3)).
   Simplifying this expression gives you (-x^2+9x-3) - (-x^2+1.5x).
   Combining like terms gives you 7.5x-3.
6. Bring down the next term from the numerator, which is 0x. Now you have (7.5x-3).
7. Divide the first term of the new expression (7.5x) by the first term of the denominator (2x). This gives you 3.75.
8. Multiply the entire denominator (2x-3) by the result from step 7 (3.75), and subtract it from the new expression (7.5x-3).
   This gives you (7.5x-3) - (3.75 * (2x-3)).
   Simplifying this expression gives you (7.5x-3) - (7.5x-11.25).
   Combining like terms gives you 8.25.
9. Since there are no more terms in the numerator, the division is complete.
   The quotient is 2x^2 - 0.5x + 3.75, and the remainder is 8.25.