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The HCF and LCM of two polynomials are (3x + 1) and (22x3 - 15x2 - 9x + 2) respectively. If one polynomial is (6x2 + 5x + 1), then what is the other polynomial?

The HCF and LCM of two polynomials are (3x + 1) and (22x3 - 15x2 - 9x + 2) respectively. If one polynomial is (6x2 + 5x + 1), then what is the other polynomial? Correct Answer <span style="">11x</span><span style=" line-height: 0; position: relative; vertical-align: baseline; top: -0.5em; font-size:10.5px;">2</span><span style=""> - 13x + 2</span>

Given:

The HCF of two polynomials = 3x + 1

The LCM of two polynomials = 22x3 - 15x2 - 9x + 2

One polynomial = 6x2 + 5x + 1

Formula used:

The product of two polynomials = Product of their HCF and LCM

Calculation:

Let the two polynomials be f(x) and g(x).

Here, f(x) = 6x2 + 5x + 1

According to the question,

f(x) × g(x) = (3x + 1) × (22x3 - 15x2 - 9x + 2)

⇒ (6x2 + 5x + 1) × g(x) = (3x + 1) × (22x3 - 15x2 - 9x + 2)

⇒ (6x2 + 2x + 3x + 1) × g(x) = (3x + 1) × (22x3 + 11x2 - 26x2 - 13x + 4x - 2)

⇒ × g(x) = (3x + 1) 

⇒ (3x + 1) × (2x + 1) × g(x) = (3x + 1) × (2x + 1) × (11x2 - 13x + 2)

⇒ g(x) = (11x2 - 13x + 2)

∴ The other polynomial is 11x2 - 13x + 2.

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