**Find Quotient and Remainder Using Synthetic Division :**

Here we are going to see some practice questions to understand the concept of finding quotient and remainder using synthetic division.

**Question 1 :**

Find the quotient and remainder for the following using synthetic division:

(i) (x^{3} + x^{2} - 7x - 3) ÷ (x - 3)

**Solution :**

Quotient = x^{2} + 4x - 3

Remainder = -12

(ii) (x^{3} + 2x^{2} - x - 4) ÷ (x + 2)

**Solution :**

Quotient = x^{2} + 0x - 1

Remainder = -2

(iii) (3x^{3} - 2x^{2} + 7x - 5) ÷ (x + 3)

**Solution :**

Quotient = 3x^{2} - 11x + 40

Remainder = -125

(iv) (8x^{4} - 2x^{2} + 6x + 5) ÷ (4x + 1)

**Solution :**

Quotient = 8x^{2} - x + 40

Remainder = -125

(iv) (8x^{4} - 2x^{2} + 6x + 5) ÷ (4x + 1)

**Solution :**

Quotient : 8x^{3} - 2x^{2} -(3x/2) + (51/8)

Remainder : 109/32

**Question 2 :**

If the quotient obtained on dividing (8x^{4} - 2x^{2} + 6x - 7) by (2x + 1) is (4x^{3} + px^{2} - qx + 3) then find p, q and also the remainder.

**Solution :**

8x^{3} - 4x2 + 0x + 6

Dividing the quotient by 2, we get

4x^{3} - 2x^{2} + 0x + 3

The value of p and q are -2 and 0 respectively and remainder is -10.

**Question 3 :**

If the quotient obtained on dividing 3x^{3} + 11x^{2} + 34x + 106 by x - 3 is 3x^{2} + ax + b, then find a, b and also the remainder.

**Solution :**

Quotient = 3x^{2} + 20x + 94

Given quotient = 3x^{2} + ax + b

a = 20 and b = 94.

After having gone through the stuff given above, we hope that the students would have understood, "Find Quotient and Remainder Using Synthetic Division"

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