FIND QUOTIENT AND REMAINDER USING SYNTHETIC DIVISION

Question 1 :

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

(i)  (x³ + x² - 7x - 3) ÷ (x - 3)

Solution :

Quotient  =  x² + 4x - 3

Remainder  =  -12

(ii)  (x³ + 2x² - x - 4) ÷ (x + 2)

Solution :

Quotient  =  x² + 0x - 1

Remainder  =  -2

(iii)  (3x³ - 2x² + 7x - 5) ÷ (x + 3)

Solution :

Quotient  =  3x² - 11x + 40

Remainder  =  -125

(iv)  (8x⁴ - 2x² + 6x + 5) ÷ (4x + 1)

Solution :

Quotient : 8x³ - 2x² -(3x/2) + (51/8)

Remainder  : 109/32

Question 2 :

If the quotient obtained on dividing (8x⁴ - 2x² + 6x - 7) by (2x + 1) is (4x³ + px² - qx + 3) then find p, q and also the remainder.

Solution :

8x³ - 4x2 + 0x + 6 

Dividing the quotient by 2, we get 

4x³ - 2x² + 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 3x³ + 11x² + 34x + 106 by x - 3 is 3x² + ax + b, then find a, b and also the remainder.

Solution :

Quotient  =  3x² + 20x + 94

Given quotient  =  3x² + ax + b

a  =  20 and b  =  94.

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