You want to divide \(x^3 - 2x^2 + 8x\) by \(x + 3\) by using synthetic division.
Which of the following is the correct setup?
-3 | 1 -2 8
-3 | 1 -2 8 0
3 | 1 -2 8 0
3 | 1 -2 8
Answer (2)
To use synthetic division to divide the polynomial x 3 − 2 x 2 + 8 x by x + 3 , we need to set up the synthetic division correctly. In synthetic division, we use the root of the divisor for the setup. Here, the divisor is x + 3 , and its root is − 3 (because x + 3 = 0 when x = − 3 ).
The coefficients of the polynomial x 3 − 2 x 2 + 8 x are 1, -2, 8, and since there's no constant term ( x 0 term), we add a 0 for it.
The correct setup for synthetic division is:
-3 \text{ | } 1 ; -2 ; 8 ; 0 ;
The correct setup for synthetic division of x 3 − 2 x 2 + 8 x by x + 3 is − 3 ∣ 1 − 2 8 0 since we use the root − 3 from the divisor and the coefficients of the polynomial. This option matches the choice: − 3 ∣ 1 − 2 8 0 .
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