Answer:
Explanation:
To divide the polynomial (8x³ + 12x² + 7) by (x + 6), we use polynomial long division.
We start by dividing the first term of the dividend (8x³) by the first term of the divisor (x). The result is 8x².
Next, we multiply the divisor (x + 6) by the result from the previous step (8x²). This gives us 8x³ + 48x².
We subtract this product from the dividend and bring down the next term (-36x²).
We then divide the new term (-36x²) by the first term of the divisor (x), which gives us -36x.
We repeat the process of multiplication, subtraction, and bringing down until we have no more terms left in the dividend.
The final result is the quotient: 8x² - 36x + 216 - (1289 / (x + 6)).
So, when we divide (8x³ + 12x² + 7) by (x + 6), we get the quotient 8x² - 36x + 216 - (1289 / (x + 6)).