DIVIDE USING POLYNOMIAL LONG DIVISION

Divide the following polynomials using long division.

Problem 1 :

(x² + x - 17) ÷ (x - 4)

Solution :

Step 1 :

In the first step, we are going to divide the first term of the dividend by the first term of the divisor.

After changing the signs, +x² and -x² will get canceled. By simplifying, we get 5x - 17.

Step 2 :

In the second step again we are going to divide the first term that is 5x by the first term of divisor that is x.

Quotient = x + 5

Remainder = 3

Problem 2 :

(3x² - 14x – 5) ÷ (x - 5)

Solution :

Quotient = 3x + 1

Remainder = 0

So, the given polynomial is divisible by (x - 5).

Problem 3 :

(x³ + x² + x + 2) ÷ (x² - 1)

Solution :

Quotient = x + 1

Remainder = 2x + 3

Problem 4 :

(7x³ + x² + x) ÷ (x² + 1)

Solution :

Quotient = 7x + 1

Remainder = - 6x - 1

Problem 5 :

(5x⁴ – 2x³ - 7x² - 39) ÷ (x² + 2x - 4)

Solution :

Quotient = 5x² - 12x + 37

Remainder = - 122x + 109

Problem 6 :

(4x⁴ + 5x - 4) ÷ (x² - 3x - 2)

Solution :

Quotient = 4x² + 12x + 44

Remainder = 161x + 84