In this page synthetic division question7 we are going to see solution of seventh problem with step by step explanation.

**Question 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**

Let
p (x) = x⁴ + 10 x³ + 35 x² + 50 x + 29 the dividend and q (x) = x + 4 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 x³ - a x² + b x + 6 to find the value of a and b.

q (x) = 0

x + 4 = 0

x = -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 (x + 4), the quotient is x³ + 6 x² + 11 x + 6 and the remainder is 5.

Quotient = x³ + 6 x² + 11 x + 6

Remainder = 5

By comparing the quotient x³ + 6 x² + 11 x + 6 with x³ - a x² + b x + 6 we get** a = -6 and b = 11**

(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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