Question

X^4-x^3-15x^2+9x+54=0

Answer 1

First write -x^3 as a difference

Your equation should look like this:

X^4➕2x^3➖3x^3➖15x^2➕9x➕54=0

Then write -15x^2 as a difference and write 9x as a sum

X^4➕2x^3➖33x^3➖6x^2➖9x^2➖18x➕27x➕54=0

Then factor out x^3 and -3x^2 along with -9x and 27

Then you factor out x➕2

(X➕2)✖️(x^3➖3x^2➖9x➕27)=0

Now factor out x^2 and -9

(x➕2)✖️(x^2✖️(x-3)-9(x-3)=0

Now factor out x-3 and split each into possible possibilities

x➕2=0

x➖3=0

x^2➖9=0

Then solve for x

You are then left with:

x1=-3, x2=-2, x3=3

Hope this helps! :3