In this page synthetic division question5 we are going to see solution of fifth problem with step by step explanation.

**Question 5**

Find the quotient and remainder using synthetic division

( 8 x⁴ - 2 x² + 6 x - 5 ) ÷ ( 4 x + 1 )

**Solution**

Let p (x) = 8 x⁴ - 2 x² + 6 x - 5 be the dividend and q (x) = 4 x + 1 be the divisor. We shall find the quotient s(x) and the remainder r, by proceeding as follows.

q (x) = 0

4 x + 1 = 0

4 x = -1

x = -1/4

**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 (4 x + 1), the quotient is 8 x³ - 2 x² - (3/2) x + (51/8) and the remainder is -211/32.

Quotient = 8 x³ - 2 x² - (3/2) x + (51/8)

Remainder = -211/32

(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

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