Answer:
[tex](2x^3+2)\div(x+3)=2x^2-6x+18-\frac{52}{(x+3)}[/tex]
Explanation:
To solve the expression using synthetic division, we will need to identify the coefficients of the dividend, so:
2x³ + 2 = 2x³ + 0x² + 0x + 2
Therefore, the coefficients are 2, 0, 0, an 2.
Additionally, since the dividend is (x + 3), which is equal to (x - (-3)) we will use the number -3.
Then, the synthetic division will be:
Where the first 2 is just moving down, then we calculate:
2 x (-3) = -6 and add then to the next coefficient.
In the same way, we get:
-6 x (-3) = 18
18 x (-3) = -54
Finally, 2 + (-54) = -52
So, the first three numbers are the coefficients of the quotient and the last number is the remainder.
Therefore, the answer to the expression is:
[tex](2x^3+2)\div(x+3)=2x^2-6x+18-\frac{52}{(x+3)}[/tex]
