How do you write #y=x^3+6x^2-25x-150# in factored form?

1 Answer
Apr 21, 2018

Answer:

#y = (x-5)(x+5)(x+6)#

Explanation:

The difference of squares identity can be written:

#A^2-B^2 = (A-B)(A+B)#

We will use this with #A=x# and #B=5#.

Given:

#y = x^3+6x^2-25x-150#

Note that the ratio between the first and second terms is the same as that between the third and fourth terms.

So this cubic will factor by grouping:

#y = x^3+6x^2-25x-150#

#color(white)(y) = (x^3+6x^2)-(25x+150)#

#color(white)(y) = x^2(x+6)-25(x+6)#

#color(white)(y) = (x^2-25)(x+6)#

#color(white)(y) = (x^2-5^2)(x+6)#

#color(white)(y) = (x-5)(x+5)(x+6)#