There are several ways to divide polynomials
The result of (4x^3-12x^2+11x+5) divided (2x-3) is 2x^2 - 3x + 1 remainder 8
First, we determine the remainder of the division
Equate 2x - 3 to 0
[tex]\mathbf{2x - 3 = 0}[/tex]
Add 3 to both sides
[tex]\mathbf{2x = 3}[/tex]
Divide both sides by 2
[tex]\mathbf{x = 1.5}[/tex]
Substitute 1.5 for x in (4x^3-12x^2+11x+5) to calculate the remainder, R
[tex]\mathbf{R= 4(1.5)^3-12(1.5)^2+11(1.5)+5}[/tex]
[tex]\mathbf{R= 8}[/tex]
Subtract 8 from (4x^3-12x^2+11x+5)
[tex]\mathbf{4x^3-12x^2+11x+5 - 8 = 4x^3-12x^2+11x-3}[/tex]
Now we divide as follows:
[tex]\mathbf{\frac{4x^3-12x^2+11x-3}{2x -3}}[/tex]
Factorize
[tex]\mathbf{\frac{4x^3-12x^2+11x-3}{2x -3} = \frac{(2x^2- 3x + 1)(2x - 3)}{2x - 3}}[/tex]
Cancel out the common factors
[tex]\mathbf{\frac{4x^3-12x^2+11x-3}{2x -3} = 2x^2- 3x + 1}[/tex]
Hence, the result of (4x^3-12x^2+11x+5) divided (2x-3) is 2x^2 - 3x + 1 remainder 8
Read more about polynomial division at:
https://brainly.com/question/8376298
