SOLUTION: A polynomial P is given a.) Factor P into linear and irreducible quadratic factors with real coefficients. b.) Factor P completely into linear factors with complex coefficients

Question 33927This question is from textbook College Algebra
: A polynomial P is given
a.) Factor P into linear and irreducible quadratic factors with real coefficients.
b.) Factor P completely into linear factors with complex coefficients
46.) P(x) = x^3-2x-4
I got: a.) (x-4)(x^2-2)
b.) (x-4)(x-2i)(x+2i) is this factored correctly?
48.) P(x) = x^4+8x^2+16
a.) (x^2+4)^2
b.) (x-2i)^2(x+2i)^2
Sorry, I'm getting mixed up with the imaginary numbers!
Thank you very much - this is a tremendous help! This question is from textbook College Algebra

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
x^2-2x-4
(x-2)(x^2+2x+2)
Using the quadratic formula on x^2+2x+2 get:
x=[-2+-sqrt(4-8)]/2
x=-1+2i or x=-1-2i
Factors are (x-2)(x+1-2i)(x+1+2i)
x^4+8x^2+16
(x^2+4)^2
(x+2i)^2(x-2i)^2
Cheers,
Stan H.

RELATED QUESTIONS
A polynomial P is given. P(x) = x^4 + 18x^2 + 81 (a) Factor P into linear and... (answered by MathLover1)

I'm not sure how to start this question. A polynomial P is given. P(x) = {{{x^4 +... (answered by josgarithmetic)

A polynomial P is given. P(x) = x^5 − 81x (a) Factor P into linear and... (answered by josgarithmetic)

Given P(x) = x^3 − 2x^2 + 9x − 18 Factor P into linear and irreducible... (answered by nyc_function)

For p(x)= 4x^5 + 4x^4 + 25x^3 - 56x^2 - 74x - 20 a. Factor into linear and irreducible (answered by drk)

Given P(x)= x^4-2x^3+7x^2-18x-18 These are the question i need help with A)show... (answered by jim_thompson5910)

Given P(x) = x^3 − 2x^2 + 9x − 18 Factor P(x) completely into linear... (answered by jsmallt9)

P(x) = x^3 + 2x^2 − 14x − 40 Factor the polynomial as a product of linear factors... (answered by MathLover1)

Factor the following expression into its linear or irreducible quadratic factors (having... (answered by robertb)