**(i) 9x ^{4} – x^{2} – 12x – 36**

**(ii) x ^{3} – 5x^{2} – x + 5**

**Answer :**

**(i) 9x**^{4} – x^{2} – 12x – 36

^{4}– x

^{2}– 12x – 36

Above terms can be written as,

9x^{4} – (x^{2} + 12x + 36)

We know that, (a + b)^{2} = a^{2} + 2ab + b^{2}

(3x^{2})^{2} – (x^{2} + (2 × 6 × x) + 6^{2})

So, (3x^{2})^{2} – (x + 6)^{2}

We know that, a^{2} – b^{2} = (a + b) (a – b)

(3x^{2} + x + 6) (3x^{2} – x – 6)

**(ii) x**^{3} – 5x^{2} – x + 5

^{3}– 5x

^{2}– x + 5

x^{3} – 5x^{2} – x + 5

Take out common in all terms,

x^{2}(x – 5) – 1(x – 5)

(x – 5) (x^{2} – 1)

(x – 5) (x^{2} – 1^{2})

We know that, a^{2} – b^{2} = (a + b) (a – b)

(x – 5) (x + 1) (x – 1)

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