Factorise x^6-7x^2-6
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x^6 - 7x² - 6
= (x²)³ - 7x² - 6
Let x² = P
= P³ - 7P - 6
= P³ + P² - P² - P -6P -6
= P²(P + 1) -P(P +1) -6(P +1)
=(P+1)(P² -P -6)
=(P+1)(P² -3P+2P -6)
=(P +1)(P-3)(P+2)
now, put P = x²
=(x² +1)(x² -3)(x² +2)
hence, (x² +1) , (x² -3) and (x²+2) are the factors of x^6 -7x² -6
= (x²)³ - 7x² - 6
Let x² = P
= P³ - 7P - 6
= P³ + P² - P² - P -6P -6
= P²(P + 1) -P(P +1) -6(P +1)
=(P+1)(P² -P -6)
=(P+1)(P² -3P+2P -6)
=(P +1)(P-3)(P+2)
now, put P = x²
=(x² +1)(x² -3)(x² +2)
hence, (x² +1) , (x² -3) and (x²+2) are the factors of x^6 -7x² -6
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