SYNTHETIC DIVISION QUESTION8

In this page synthetic division question8 we are going to see solution of seventh problem with step by step explanation.

Question 8

(8) If the quotient on dividing (8 x⁴ - 2 x² + 6 x - 7) by (2 x + 1) is

4 x³ + p x² - q x + 3, then find p, q and also the remainder.

Solution

Let p (x) = 8 x⁴ - 2 x² + 6 x - 7 the dividend and q (x) = 2 x + 1 be the divisor. We shall find the quotient s(x) and the remainder r, by proceeding as follows.After getting quotient we have to compare that with the equation 4 x³ + p x² - q x + 3 to find the value of p and q.

q (x) = 0

2 x + 1 = 0

2 x = -1

x = -1/2

Step 1:  Arrange the dividend and the divisor according to the descending powers of x and then write the coefficients of dividend in the first zero. Insert 0 for missing terms.

Step 2:  Find out the zero of the divisor.

Step 3:  Put 0 for the first entry in the second row.

Step 4:  Write down the quotient and remainder accordingly. All the entries except the last one  in the third row constitute the coefficients of the quotient.

When P (x) is divided by (x + 4), the quotient is 8 x³ - 4 x² + 0 x + 6 and the remainder is -10.

Quotient = 8 x³ - 4 x² + 0 x + 6

Remainder = -10

By dividing the quotient by 2,we get 4 x³ - 2 x² + 0 x + 3

By comparing the quotient 4 x³ - 2 x² + 0 x + 3 with 4 x³ + p x² - q x + 3 we get p = -2 and q = 0

(1) Find the quotient and remainder using synthetic division  ( x³ + x² - 3 x + 5 ) ÷ ( x - 1 )   Solution

(2) Find the quotient and remainder using synthetic division ( 3 x³ - 2 x² + 7 x - 5 ) ÷ ( x + 3 )   Solution

(3) Find the quotient and remainder using synthetic division ( 3 x³ + 4 x² - 10 x + 6 ) ÷ ( 3 x - 2 )  Solution

(4) Find the quotient and remainder using synthetic division ( 3 x³ - 4 x² - 5 ) ÷ ( 3 x + 1 )  Solution

(5) Find the quotient and remainder using synthetic division ( 8 x⁴ - 2 x² + 6 x - 5 ) ÷ ( 4 x + 1 )   Solution

(7) If the quotient on dividing (x⁴ + 10 x³ + 35 x² + 50 x + 29) by (x + 4) is x³ - a x² + b x + 6, then find a, b and also the remainder.   Solution

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