**SYNTHETIC DIVISION QUESTION4**

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In this page synthetic division question4 we are going to see solution of fourth problem with step by step explanation.

**Question 4**

Find the quotient and remainder using synthetic division

( 3 x³ - 4 x² - 5 ) ÷ ( 3 x + 1 )

**Solution**

Let
p (x) = 3 x³ - 4 x² - 5 be the dividend and q (x) = 3 x + 1 be the
divisor. We shall find the quotient s(x) and the remainder r, by
proceeding as follows.

q (x) = 0

3 x + 1 = 0

3 x = - 1

x = -1/3

**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 (3x + 1), the quotient is 3 x² - 5 x + 5/3 and the remainder is -50/9.

Quotient = 3 x² - 5 x + 5/3

Remainder = -50/9

(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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