Divide as directed (x4 – 81) ÷ (x3 + 3x2 + 9x + 27)
(x4 – 81) ÷ (x3 + 3x2 + 9x + 27)
x4 – 81 = (x2)2 – (9)2 = (x2 + 9) (x2 – 9)
= (x2 + 9) [(x)2 – (3)2]
= (x2 + 9) (x + 3) (x – 3)
And,
x3 + 3x2 + 9x + 27 = (x)2 + (x + 3) + 9 (x + 3)
= (x2 + 9) (x + 3)
Now,
= (x – 3)
Divide as directed (3x3 – 6x2 – 24x) ÷ (x – 4) (x + 2)
Divide as directed 15(y + 3)(y2 – 16) ÷ 5(y2 – y – 12)
Factorise x2 + 2xy – 99y2
Factorise 6x2 – 5xy – 6y2
Factorise 2x2 – x – 6
