The HCF of 21 xx2-1 and 3 x3x-1 is-A- 3 xx-1B- 3 xx-1- 21 x x -1D- 21 xx-1

The correct option is A 3x(x+1)21x(x^2 1) = 3× 7× x× (x+1)(x 1). 3x^3(x+1) = 3× x^3× (x+1). Hence, the common irreducible factors between 21x(x^2 1) and 3x^3 ...

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Standard X

Mathematics

GCD of Polynomials

The HCF of 21...

Question

The HCF of $21 x (x^{2} - 1) a n d 3 x^{3} (x + 1)$ is:

3 x (x + 1)

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3 x (x - 1)

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21 x (x + 1)

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21 x (x - 1)

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Solution

The correct option is A $3 x (x + 1)$
$21 x (x^{2} - 1) = 3 \times 7 \times x \times (x + 1) (x - 1)$ .
$3 x^{3} (x + 1) = 3 \times x^{3} \times (x + 1)$ .
Hence, the common irreducible factors between $21 x (x^{2} - 1) a n d 3 x^{3} (x + 1)$ are 3,x and (x+1).
The least exponents of these factors are respectively 1,1 and 1.
Hence, the HCF = $3^{1} \times x^{1} \times (x + 1)^{1} = 3 x (x + 1)$ .

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Similar questions

Q. Find the H.C.F of

21 x (x^{2} - 1)

and

3 x^{3} (x + 1)

Q. If

f (x) = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & x & x + 1 2 x & x (x - 1) & (x + 1) x 3 x (x - 1) & x (x - 1) (x - 2) & (x + 1) x (x - 1) \end{matrix} ∣ ∣ ∣ ∣ ∣

,

Then,

f (100)

is equal to

cot x cot 2x – cot 2x cot 3x – cot 3x cot x = 1

\lim_{x \to 0} \frac{\sqrt{1 + 3 x} - \sqrt{1 - 3 x}}{x}

Q. Simplify

(\sqrt{x} - 3 x) (x + \frac{1}{x})

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The HCF of 21x(x2−1) and 3x3(x+1) is:

The correct option is A 3x(x+1)21x(x2−1)=3× 7× x× (x+1)(x−1). 3x3(x+1)=3× x3× (x+1). Hence, the common irreducible factors between 21x(x2−1) and 3x3(x+1) are 3,x and (x+1). The least exponents of these factors are respectively 1,1 and 1. Hence, the HCF = 31× x1× (x+1)1=3x(x+1).

The HCF of $21 x (x^{2} - 1) a n d 3 x^{3} (x + 1)$ is: