# Factor out

1) Factor the polynomial completely.

P(x) = x^2 + 9

P(x) =

Find all its zeros. State the multiplicity of each zero. (If an answer does not exist, enter DNE.)

real zero x=______ with multiplicity______

complex zero x=_______(positive imaginary part) with multiplicity ____

complex zero x=_______(negative imaginary part) with multiplicity _____

2) Factor the polynomial completely.

Q(x) = x^2 + 2x + 2

Q(x) =

Find all its zeros. State the multiplicity of each zero. (If an answer does not exist, enter DNE.)

real zero x=______ with multiplicity _______

complex zero x=_____ (positive imaginary part) with multiplicity ______

complex zero x=_______(negative imaginary part) with multiplicity _______

3)factor the polynomial completely.

Q(x) = x^4 â?' 256

Q(x) =

Find all its zeros. State the multiplicity of each zero. (If an answer does not exist, enter DNE.)

real zero x=_______(smaller value) with multiplicity ______

real zero x=_______(larger value) with multiplicity ______

complex zero x=________(positive imaginary part) with multiplicity ______

complex zero x=_______(negative imaginary part) with multiplicity______

4) Factor the polynomial completely.

Q(x) = x^4 + 18x^2 + 81

Q(x) =

Find all its zeros. State the multiplicity of each zero. (If an answer does not exist, enter DNE.)

real zero x=______ with multiplicity __________

complex zero x=____ (positive imaginary part) with multiplicity ___________

complex zero x=______ (negative imaginary part) with multiplicity __________

5) Find all zeros of the polynomial. (Enter your answers as a comma-separated list. If a root has multiplicity greater than one, only enter the root once.)

P(x) = x^3 â?' 9x^2 + 25x â?' 25

x =

#### Solution Preview

1) The equation x^2+9=0 can be written as x^2=-9. We then have x = sqrt(-9) or x = -sqrt(9), so x = 3i or x = -3i. The multiplicity of each root is 1, and 3i has positive imaginary part (3), while the other one has negativeimaginary part (-3). In general, the imaginary part of a complex number a+bi is b, the coefficient at the imaginary unit i.

2) Solving x^2+2x+2=0 as a quadratic equation, we get

D = (2)^2 - 4*1*2 = 4-8 = -4

x1 = [(-2)+sqrt(-4)]/2 = (-2+2i)/2 = -1+i

x2 = [(-2)-sqrt(-4)]/2 = (-2+2i)/2 = ...

#### Solution Summary

Factoring out is depicted.