Answer:
[tex]\frac{125x^3 - 8}{5x - 2} = 25x^2 + 10x +4[/tex]
Step-by-step explanation:
Given
[tex]Dividend = 125x^3 - 8[/tex]
[tex]Divisor = 5x - 2[/tex]
Required
Determine the quotient
See attachment for complete process.
First, divide 125x^3 by 5x
[tex]\frac{125x^3}{5x} =25x^2[/tex]
Write [tex]25x^2[/tex] at the top
Multiply [tex]5x - 2[/tex] by [tex]25x^2[/tex]
[tex]= 125x^3 - 50x^2[/tex]
Subtract from 125x^3 - 8
i.e.
[tex]125x^3 - 8 - (125x^3 - 50x^2) = 50x^2 - 8[/tex]
Step 2:
Divide 50x^2 by 5x
[tex]\frac{50x^2}{5x} = 10x[/tex]
Write [tex]10x[/tex] at the top
Multiply [tex]5x - 2[/tex] by [tex]10x[/tex]
[tex]= 50x^2 - 20x[/tex]
Subtract from 50x^2 - 8
i.e.
[tex]50x^2 - 8 - (50x^2 - 20x) = 20x - 8[/tex]
Step 3:
Divide 20x by 5x
[tex]\frac{20x}{5x} = 4[/tex]
Write [tex]4[/tex] at the top
Multiply [tex]5x - 2[/tex] by [tex]4[/tex]
[tex]= 20x - 8[/tex]
Subtract from 20x - 8
i.e.
[tex]20x - 8 - (20x - 8) = 0[/tex]
Hence:
[tex]\frac{125x^3 - 8}{5x - 2} = 25x^2 + 10x +4[/tex]
