Question

Factorise and find the HCF of the following pairs of polynomials:-
4x^3(x^3+27)and 10x^5(x^2+6x+9)​

Answer 1

Answer:

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Answer 2

Answer:

The HCF of the polynomials = 2x³(x+3)

Step-by-step explanation:

To find,

The HCF of the polynomials 4x³(x³+27)and 10x⁵(x²+6x+9)​

Recall the formula

a³+b³ = (a+b)(a² - ab+b²)

(a+b)² = a²+2ab+b²

Solution:

By applying the formula a³+b³ = (a+b)(a² - ab+b²), we get

x³+27 = (x+3)(x²-3x+9)

∴4x³(x³+27) = 4x³(x+3)(x²-3x+9)

By applying the formula(a+b)² = a²+2ab+b², we get

(x²+6x+9)​ = (x+3)²

10x⁵(x²+6x+9)​ = 10x⁵ (x+3)²

The factorization of 4x³(x³+27) = 2×2×x×x×x×(x+3)(x²-3x+9)

The factorization of 10x⁵(x²+6x+9)​ = 2×5×x×x×x×x×x×(x+3)²

The common factors of  4x³(x³+27)and 10x⁵(x²+6x+9)​ are

2,x,x,x,(x+3)

The highest common factor is = 2x³(x+3)

∴ The HCF of the polynomials = 2x³(x+3)

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