Question

find the GCD of x³+2x²-3x and 2x³+5x²-3x​

Answer 1

Answer :

GCD = x(x + 3) OR x² + 3x

Solution :

• Given polynomials are :

x³ + 2x² - 3x and 2x³ + 5x² - 3x

• To find : GCD (Greatest Common Divisor)

Let's factorize x³ + 2x² - 3x

→ x³ + 2x² - 3x

→ x(x² + 2x - 3)

→ x(x² + 3x - x - 3)

→ x[x(x + 3) - (x + 3)]

→ x(x + 3)(x - 1)

Now ,

Let's factorize 2x³ + 5x² - 3x

→ 2x³ + 5x² - 3x

→ x(2x² + 5x - 3)

→ x[2x² + 6x - x - 3)

→ x[2x(x + 3) - (x + 3)]

→ x(x + 3)(2x - 1)

Clearly ,

The common factors in both the polynomials are x and (x + 3) .

Hence ,

GCD = x(x + 3) OR x² + 3x

Answer 2

Answer:

Step-by-step explanation: