Factorize algebraic expressions: y^{2} + 5y – 36

We have,

y^{2} + 5y – 36

By considering, p+q = 5 and pq = -36

So we can replace 5y by 9y – 4y

-36 by 9 × -4

y^{2} + 5y – 36 = y^{2} + 9y – 4y – 36

= y (y + 9) – 4 (y + 9)

= (y – 4) (y + 9)

Divide as directed (x^{4} – 81) ÷ (x^{3} + 3x^{2} + 9x + 27)

Divide as directed (3x^{3} – 6x^{2} – 24x) ÷ (x – 4) (x + 2)

Divide as directed 15(y + 3)(y^{2} – 16) ÷ 5(y^{2} – y – 12)

Factorise x^{2} + 2xy – 99y^{2}

Factorise 6x^{2} – 5xy – 6y^{2}