Q1 of 227 Page 92

Find the LCM of each pair of the following polynomials.

2x3 + 15x2 + 2x – 35, x3 + 8x2 + 4x – 21 whose GCD is x + 7.

Given: –


Polynomials 2x3 + 15x2 + 2x – 35 , x3 + 8x2 + 4x – 21


And GCD[Greatest Common Divisor] = (x + 7)


Formula used: –


The product of 2 polynomial is equal to product of their LCM


and GCD.


Product of 2 polynomial = LCM × GCD


Product of 2 polynomial = (2x3 + 15x2 + 2x – 35) × (x3 + 8x2 + 4x – 21)


Product of 2 polynomial = LCM × GCD


LCM =


LCM =


LCM =


LCM = (2x2 + x – 5)(x3 + 8x2 + 4x – 21)


Conclusion: –


The LCM of given polynomials [2x3 + 15x2 + 2x – 35 , x3 + 8x2 + 4x – 21] is (2x2 + x – 5)(x3 + 8x2 + 4x – 21)


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