How do you factor x^3 - 12x^2 + 35x?

2 Answers
Apr 22, 2018

The answer is x(x-5)(x-7).

Explanation:

First we take out the common factor x:
x^3-12x^2+35x=x(x^2-12x+35)

Then we use the quadratic formula:
x=\frac {-b\pm (\sqrt {b^{2}-4ac\ })}{2a}

x=\frac {-(-12)\pm (\sqrt {(-12)^{2}-4*1*35\ })}{2*1}

x=\frac {12\pm (\sqrt {144-140\ })}{2}

x=\frac {12\pm \sqrt {4)}{2}

x=\frac {12\pm \2}{2}

x_1=5

x_2=7

ax^2+bx+c=a*(x-x_1)(x-x_2)

Then we just write this instead of the quadratic equation we've just solved:

x^3-12x^2+35x=x(x-5)(x-7)

Apr 22, 2018

x(x -7)(x -5)

Explanation:

Start by taking out the common factor of x

x^3 -12x^2 +35x

=x(x^2-12x+35)

Now factor the quadratic trinomial.

Find factors of 35 which add to make 12

7 xx 5 will do nicely: 7xx5=35 and 7+5=12

x(x" "7)(x" "5)

For the signs, they both have to be the same to get +35, but they need to add to -12

x(x -7)(x -5)