Question

find the GCD of the polynomials
45(x⁴ - x³ - x²) and 75(8x⁵ + x²)​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given:

$45( {x}^{4} - {x}^{3} - {x}^{2} ) \: and \: 75(8 {x}^{5} + {x}^{2})$

To find: Find GCD of given polynomials.

Solution:

Step 1: Take common factor of 1st polynomial

$45( {x}^{4} - {x}^{3} - {x}^{2} ) \\ = 15 {x}^{2} \times 3 ( {x}^{2} - x - 1)$

Step 2: Take common factor of 2nd polynomial

$75( {x}^{5} + {x}^{2} ) \\ = 15 {x}^{2} \times 5 (8 {x}^{3} + 1)$

Step 3: To find HCF or GCD search for common factors in both polynomial

$15 {x}^{2}$

Final answer:

HCF of $45( {x}^{4} - {x}^{3} - {x}^{2} ) \: and \: 75(8 {x}^{5} + {x}^{2})$ is $\bold{\red{15x^2}}$

Hope it helps you.