Factorise x-3 - 1-3 - Maths Q-A

We have to find the factors of x^3 1:x^3 10ex0ex=x^3 1^30ex0ex=(x 1)(x^2+x+1) [∵a^3 b^3=(a b)(a^2+ab+b^2]Hence, the factors of the polynomial x^3 1 are (x 1 ...

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Standard VIII

Mathematics

Factorizing a Term

Factorise x^3...

Question

Factorise $x^{3} - 1$

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Solution

We have to find the factors of $x^{3} - 1$ :
$x^{3} - 1 = x^{3} - 1^{3} = (x - 1) (x^{2} + x + 1) [∵ a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2}]$
Hence, the factors of the polynomial $x^{3} - 1$ are $(x - 1)$ and $(x^{2} + x + 1)$ .

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Factorise x3-1

We have to find the factors of x3-1:x3-1=x3-13=(x-1)(x2+x+1)[∵a3-b3=(a-b)(a2+ab+b2]Hence, the factors of the polynomial x3-1 are x-1 andx2+x+1.

Factorise $x^{3} - 1$

We have to find the factors of $x^{3} - 1$ :
$x^{3} - 1 = x^{3} - 1^{3} = (x - 1) (x^{2} + x + 1) [∵ a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2}]$
Hence, the factors of the polynomial $x^{3} - 1$ are $(x - 1)$ and $(x^{2} + x + 1)$ .