CHING WAI 發問於 科學及數學數學 · 1 十年前

# dividing polynomials 2 --------urgent

1. (a^4 +a^2b^2 +b^4 ) / (a^2 + ab +b^2 ) (152b)&lt;---no need to care about this

2. (2a^3 +a^2 - 5a +2) / (a+1) (153b)

3. (x^2 -3xy +2y^2 +3x - 6y -8) / (x-y+4) (153b)

4. divide x^3 +4x^2 - 5x+3 by x-2 (154a)

5. using the result of (4), write the relatioship between x^3 + 4x^2 -5x +3 and x-2 (154a)

( Ans. x^3 +4x^2 -5x +3 = ?????????????? )

### 1 個解答

• 1 十年前
最愛解答

1. (a^4 +a^2b^2 +b^4 ) / (a^2 + ab +b^2 )

a^2 -ab + b^2

a^2+ab+b^2 | a^4 + a^2b^2 + b^4

a^4 + a^3b+a^2b^2

- a^3b + b^4

- a^3b - a^2b^2 - ab^3

a^2b^2 + ab^3 + b^4

a^2b^2 + ab^3 + b^4

So, the answer is (a^2 - ab + b^2)

2. (2a^3 +a^2 - 5a +2) / (a+1)

If the dividing is a+1 , it will not complete to divided.

So, it may be dividing a-1

2a^2 - a - 4

a + 1 | 2a^3 + a^2 -5a + 2

2a^3 + 2a^2

- a^2 - 5a + 2

- a^2 - a

- 4a + 2

- 4a - 4

6

2a^2 + 3a - 2

a - 1 | 2a^3 + a^2 -5a + 2

2a^3 + 2a^2

3a^2 - 5a + 2

3a^2 - 3a

- 2a + 2

- 2a + 2

So the answer will be (2a^2 - a - 4) and remind 6

or (2a^2 + 3a -2)

3. (x^2 -3xy +2y^2 +3x - 6y -8) / (x-y+4)

x - 2y - 1

x - y + 4 | x^2 - 3xy + 2y^2 + 3x - 6y - 8

x^2 - xy + 4x

- 2xy + 2y^2 -x -6y -8

- 2xy + 2y^2 - 8y

-x + 2y - 8

-x + y - 4

y - 4

So the answer is (x-2y-1) and remind (y-4)

4. divide x^3 +4x^2 - 5x+3 by x-2

x^2 + 6x + 7

x - 2 | x^3 + 4x^2 - 5x + 3

x^3 - 2x^2

6x^2 - 5x + 3

6x^2 -12x

7x + 3

7x - 14

17

so the answer is (x^2 +6x + 7 ) and remind 17

5. using the result of (4), write the relatioship between x^3 + 4x^2 -5x +3 and x-2

x^3 +4x^2 -5x +3 = (x - 2)(x^2 +6x + 7 ) + 17

資料來源： Me