Answer :

**Concept Used:**

x^{2} – a^{2} = (x + a)(x – a)

**Explanation:**

x^{8} – 256 = (x)^{8} – (2)^{8}

x^{8} – 256 = (x^{4})^{2} – (2^{4})^{2}

x^{8} – 256 = (x^{4} + 2^{4})(x^{4} – 2^{4})

x^{8} – 256 = (x^{4} + 16)((x^{2})^{2} – (2^{2})^{2})

x^{8} – 256 = (x^{4} + 16)(x^{2} + 4)(x^{2} – 4)

**x ^{8} – 256 = (x^{4} + 16)(x^{2} + 4)(x + 2)(x – 2)**

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Factorize:

x^{3} – 2x^{2}y + 3xy^{2} – 6y^{3}

Find the value of a for which the polynomial is divisible by (x+3).

RS Aggarwal & V Aggarwal - MathematicsFactorize:

a^{2} + a – 3a^{2} - 3

Factorize:

2a(x + y) -3b(x + y)

RS Aggarwal & V Aggarwal - MathematicsFactorize:

8 – 4a – 2a^{3} + a^{4}

If 𝑎 + 𝑏 + 𝑐 = 9 and 𝑎𝑏 + 𝑏𝑐 + 𝑐𝑎 = 26, find 𝑎^{2} + 𝑏^{2} + 𝑐^{2}.

In each of the following, use factor theorem to find whether polynomial *g*(*x*) is a factor of polynomial *f*(*x*) or, not:

*f*(*x*) = *x*^{3}-6*x*^{2}+11*x*-6, *g*(*x*) = *x*-3

Show that p – 1 is a factor of p^{10} – 1 and also of p^{11} – 1.

Factorize:

a^{2} + ab(b + 1) + b^{3}