Question

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

Answer 1

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

Answer 2

$\frac{15x^{2} - 24x + 9}{3x - 3} = \frac{3(5x^{2}) - 3(8x) + 3(3)}{3(x) - 3(1)} = \frac{3(5x^{2} - 8x + 3)}{3(x - 1)} = \frac{5x^{2} - 5x - 3x + 3}{x - 1} = \frac{5x(x) - 5x(1) - 3(x) - 3(-3)}{x - 1} = \frac{5x(x - 1) - 3(x - 1)}{x - 1} = \frac{(5x - 3)(x - 1)}{x - 1} = 5x - 3$