Final Answer:
The result of dividing (6x² +42x+39) by (x+6) is 6x+1.
Step-by-step explanation:
6x + 1
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x + 6 | 6x^2 + 42x + 39
- (6x^2 + 36x)
6x + 39
- (6x + 36)
3
Divide 6x^2 by x to get 6x.
Multiply (x + 6) by 6x to get 6x^2 + 36x and subtract it from 6x^2 + 42x + 39, leaving 6x + 39.
Repeat the process by dividing 6x into 6x + 39, resulting in 1.
Multiply (x + 6) by 1 to get x + 6 and subtract it from 6x + 39, leaving a remainder of 3.
Therefore, (6x^2 + 42x + 39) ÷ (x + 6) equals 6x + 1 with a remainder of 3.