find the GCD of x³+2x²-3x and 2x³+5x²-3x
Answers
Answered by
10
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
Answered by
0
Answer:
Step-by-step explanation:
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