Use long division to find the quotient of:

[tex]\frac{12x^3 + 3x^2 - 108}{3x - 6}[/tex]

3 x − 6 12 x 3 + 3 x 2 − 108 ​ = 3 ( x − 2 ) 3 ( 4 x 3 + x 2 − 36 ) ​ = x − 2 4 x 3 + x 2 − 9 x 2 + 9 x 2 − 36 ​ = = x − 2 4 x 3 − 8 x 2 + 9 x 2 − 36 ​ = x − 2 4 x 2 ( x − 2 ) + 9 ( x 2 − 4 ) ​ = = x − 2 4 x 2 ( x − 2 ) + 9 ( x − 2 ) ( x + 2 ) ​ = x − 2 ( x − 2 ) [ 4 x 2 + 9 ( x + 2 )] ​ = = 4 x 2 + 9 ( x + 2 ) = 4 x 2 + 9 x + 18

Answered by Lilith | 2024-06-10

Using long division, we find that the quotient of 3 x − 6 12 x 3 + 3 x 2 − 108 ​ is 4 x 2 + 9 x + 18 and there is no remainder.
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Answered by Lilith | 2024-10-01