Question

Divide using synthetic division. State what the remainder means. You must use synthetic division as shown in class for full credit. SHOW ALL STEPS FOR FULL CREDIT! ( 2x^4-3x^2+4x-9) / (x+2)

Answer 1

`2x^(3)-4x^(2)+5x-6+(3)/(x+3)`

Explanation:

Given expression is (2x⁴ - 3x² + 4x - 9).

We have to divide this expression by (x + 2) by using synthetic division.

Expression given above can be written as,

2x⁴ - 3x² + 4x - 9 = 2x⁴ + 0.x³ - 3x² + 4x - 9

Now divide by x = -2 by synthetic division method.

-2 | 2 0 -3 4 -9

- -4 8 -10 12

2 -4 5 -6 3

Remainder of the synthetic division will be (3).

So we rewrite the given expression as,

`2x^(3)-4x^(2)+5x-6+(3)/(x+3)`