Question

Simplify (15x2 – 24x + 9) ÷ (3x – 3) = ?

Answer 1

`(15x^(2) - 24x + 9)/(3x - 3) = (3(5x^(2)) - 3(8x) + 3(3))/(3(x) - 3(1)) = (3(5x^(2) - 8x + 3))/(3(x - 1)) = (5x^(2) - 5x - 3x + 3)/(x - 1) = (5x(x) - 5x(1) - 3(x) - 3(-3))/(x - 1) = (5x(x - 1) - 3(x - 1))/(x - 1) = ((5x - 3)(x - 1))/(x - 1) = 5x - 3`

Answer 2

factor 15x^2-24x+9
we know that we are supposed to divide by (3x-3) so that might be one of the factors
(3x-3)(ax+y)
a must be 5 since 5 times 3=15
(3x-3)(5x+y)
y must be -3 because -3 times -3=9 so
(3x-3)(5x-3)
try to multiply and get
15x^2-15x-9x+9=15x^2-24x+9
true

now we have
[(3x-3)(5x-3)]/(3x-3)=(3x-3)/(3x-3) times (5x-3)/1=1 times 5x-3
answer is 5x-3