Question

Factor: 10x^2-15x=0 ?

Answer 1

Like every quadratic equation

$ax^2+bx+c=0$

where $c=0$

$ax^2+bx=0$

we can factor out $x$

$x(ax+b)=0$

And find the two solutions

$x=0,\quad x=-\dfrac{b}{a}$

In this case, the solutions are

$x=0,\quad x=\dfrac{3}{2}$

If you know that $x_1,\ x_2$ are the solutions to the quadratic equation

$ax^2+bx+c=0$

then you can factor the poynomial as

$a(x-x_1)(x-x_2)$

So, in this case, you have

$10x^2-15x = 10(x-0)\left(x-\dfrac{3}{2}\right)=10x\left(x-\dfrac{3}{2}\right)$