Q1 of 227 Page 92

Find the LCM of each pair of the following polynomials.

2x3 – 3x2 – 9x + 5, 2x4 – x3 – 10x2 – 11x + 8 whose GCD is 2x – 1

Given: –


Polynomials 2x3 – 3x2 – 9x + 5, 2x4 – x3 – 10x2 – 11x + 8


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 – 3x2 – 9x + 5) × (2x4 – x3 – 10x2 – 11x + 8)


Product of 2 polynomial = LCM × GCD


LCM =


LCM =


LCM =


LCM = (x3 – 5x – 8)( 2x3 – 3x2 – 9x + 5)


Conclusion: –


The LCM of given polynomials [2x3 – 3x2 – 9x + 5, 2x4 – x3 – 10x2 – 11x + 8] is (x3 – 5x – 8)( 2x3 – 3x2 – 9x + 5)


More from this chapter

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1

Find the LCM of each pair of the following polynomials.

x4 + 3 x3 + 6 x2 + 5x + 3, x4 + 2 x2 + x + 2 whose GCD is x2 + x + 1

 1

Find the LCM of each pair of the following polynomials.

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

 2

Find the other polynomial q(x) of each of the following, given that LCM and GCD and one polynomial p(x) respectively.

(x + 1)2 (x + 2)2, (x + 1) (x + 2), (x + 1)2 (x + 2)

 2

Find the other polynomial q(x) of each of the following, given that LCM and GCD and one polynomial p(x) respectively.

(4x + 5)3 (3x – 7)3, (4x + 5) (3x – 7)2, (4x + 5)3 (3x – 7)2