Question

Divide 4x3 + 2x2 + 5x – 6 by 2x2 + 1 + 3x and verify the division algorithm.

Answer 1

Answer:

hope it helps

Step-by-step explanation:

remainder = 9x-4

quotient =2x-2.

Answer 2

Concept:

The division algorithm is the algorithm in which the product of quotient and divisor is added up with the remainder to get the dividend.

Dividend=(Divisor×quotient)+Remainder

Given:

Dividend: 4x³ + 2x² + 5x – 6

Divisor: 2x²+3x+1

Find:

Verify the division algorithm.

Solution:

Dividing the 4x³ + 2x² + 5x – 6 by 2x²+3x+1 and calculating the quotient and remainder.

Quotient: 2x–2

Remainder: 9x–4

The division algorithm is defined as:

Dividend=(Divisor×quotient)+Remainder

As the

Dividend: 4x³ + 2x² + 5x – 6

Divisor: 2x²+3x+1

Checking by substituting in Dividend=(Divisor×quotient)+Remainder:

4x³ + 2x² + 5x – 6=[(2x² +3x+ 1)×(2x–2)] +(9x–4)

4x³ + 2x² + 5x – 6=[4x³– 4x²+6x²–6x+2x –2 ]+(9x–4)

4x³ + 2x² + 5x – 6=[4x³+2x²–4x –2 ]+(9x–4)

4x³ + 2x² + 5x – 6=4x³+2x²–4x +9x–2–4

4x³ + 2x² + 5x – 6=4x³ + 2x² + 5x – 6

As the left-hand side is equal to the right-hand side. Hence, the division algorithm is verified.

#SPJ2