Question

45(x4-x³-x²) and 75(8x5+x²)​

Answer 1

Step-by-step explanation:

*Given:

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

To find: Find HCF 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

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

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.

*Note: Question is incomplete.

To learn more on brainly:

find the GCD of the polynomials

45(x⁴ - x³ - x²) and 75(8x⁵ + x²)

https://brainly.in/question/19891554