Question

Divide ( x^5- 2x^3 + 8 ) ÷ ( x^2 – x – 2 )

Answer 1

Answer:

Equation at the end of step 1 :

((x5) - 2x3) - 8x = 0

Step 2 :

Step 3 :

Pulling out like terms :

3.1 Pull out like factors :

x5 - 2x3 - 8x = x • (x4 - 2x2 - 8)

Trying to factor by splitting the middle term

3.2 Factoring x4 - 2x2 - 8

The first term is, x4 its coefficient is 1 .

The middle term is, -2x2 its coefficient is -2 .

The last term, "the constant", is -8

Step-1 : Multiply the coefficient of the first term by the constant 1 • -8 = -8

Step-2 : Find two factors of -8 whose sum equals the coefficient of the middle term, which is -2 .

-8 + 1 = -7

-4 + 2 = -2 That's it

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Answer 2

Answer:

Set up the long division.

Notice the 0's put in as place

holders for missing powers of x.

x2 = x4

x2 .

Choose x2 since

x2 · x2 matches x4.

x4 + 0x3- 3x2 = x2(x2 + 0x - 3).

Subtract x4 + 0x3 - 3x2 from

x4 - 2x3 + 0x2 + 8x - 14.

Result is -2x3 + 3x2 + 8x - 14.

-2x = -2x3

x2 .

Choose -2x since

-2x · x2 matches -2x3.

-2x3 + 0x2 + 6x = -2x(x2 + 0x - 3).

Subtract -2x3 + 0x2 + 6x from

-2x3 + 3x2 + 8x - 14..

Result is 3x2 + 2x - 14.

3 = 3x2

x2 .

Choose 3 since

3 · x2 matches 3x2.

3x2 + 0x2 - 9 = 3(x2 + 0x - 3).

Subtract 3x2 + 0x2 - 9 from

3x2 + 2x - 14..

Result is 2x - 5.

2x - 5 is the remainder.

Answer: x4 - 2x3 + 8x - 14

x2 - 3 = x2 - 2x + 3 + 2x - 5

x2 - 3 .

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