Factor out
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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 =
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Solution Summary
Factoring out is depicted.
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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 = ...
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