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

Answer:

$2x^{3}-4x^{2}+5x-6+\frac{3}{x+3}$

Step-by-step 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,

$2x^{3}-4x^{2}+5x-6+\frac{3}{x+3}$

Answer 2

Answer:

Remainder: -24

Step-by-step explanation:

First we have to divide → 3x^3 + x^2 - 4 / x - 2

We will get → 3x^2 + 7x + 14 + 24/x-2

So the remainder is -24