Question

Find zero of the polynomial:
x^4+x^3+x^2-9=0

Answer 1

Answer:

If you can't find the factoring by looking at this, simplify the equation.

let x2=y to make things easier to see

Now we have y2−8y−9=0

See it now?

We can factor into (y−9)(y+1)

Now substitute back in x2 for y.

(x2−9)(x2+1)

Since (x2−9) is a difference of two squares,

(x−3)(x+3)

Now we have (x−3)(x+3)(x2+1)

x can be 3, -3 for the first two parts

x2+1=0 can become x2=−1

Taking the positive and negative root means x=±√−1

Thus x=±i in addition to 3 and -3.

Step-by-step explanation:

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