Factor each of the following completely Factor each of the f

Factor each of the following completely

Factor each of the following completely 6ab + 9a^2 b - 15a^3 b 9p - 3pq + 2nq - 6n 12x^2 y - 36xy^2 + 27y^3 y^4 - 2y^2 - y^3 x^3 y - xy + 5x^2 y - 5y 42x^3 + 68x^2 + 16x

Solution

4) 6ab + 9a^2b - 15a^3b

Taking out common factor : 3ab( 2 + 3a - 5a^2)

3ab( - 5a^2 + 3a +2) = 3ab( -5a^2 + 5a -2a +2)

= 3ab(5a( -a +1) +2( -a +1) )

= 3ab(5a+2)( 1-a)

11) y^4 -2y^2 - y^3

= y^2( y^2 - y -2)

y^2( y^2 -2y +y -2)

= y^2(y -2)(y+1)

15) 9p - 3pq + 2nq -6n

(9p - 3pq) + (2nq -6n)

Taking out common factors 3p( 3 -q) +2n( q - 3)

-3p( q -3) +2n( q -3)

(-3p +2n)( q -3)