factoring
posted by kristie .
can this equation be factored further?
y= x^4+2x^3+4x^2+8x+16
Not in the real number system. If you plot the function, you will see the minimum is at x=1.1 (approx) and y is positive. At no x does the function equal zero, so there are no real roots, which means, no factors.
You can do some moving around..
x^4+2x^3+4x^2+8x+16
x^3(x + 2) + 4x(x + 2) + 16
(x+2)(x^3+ 4x) + 16
x(x +2)(x^2+4) + 16
I don't personally see that as progress.
Not having real roots doesn't mean it can't be factored: x^4+2x^2+1=(x^2+1)^2 has no real roots, but it does factor.
In theory every polynomial over R factors as polynomials of degree 1 or 2, but finding the factors can be time consuming in practice.
True.
Respond to this Question
Similar Questions

MATH,HELP
Can someone show me how to even do this problem. Find all positive values for K for which each of the following can be factored. x^2 + x  k News flash: It can be factored with any term (although the roots may not be real roots). Now … 
math
Which three options are true about the quadratic equation? 
algebra
Find all positive values for k for which each of the following can be factored. x^2+3x+kthe coefficent of the middle term is 3 3=2+1 k=2*1=2 did i do this right This one I had no Idea where to start can some one please explain it to … 
Algebra
Find all positive values for k for which each of the following can be factored. X^2xk (Your answer seems to be the same as the other problem x^2+xk ) Is this correct too? 
Math  Real number system
Solve the following equation in the real number system. Please show all of your work. x^4 + 6x^3 + x^2  24x  20 = 0 Help!!!! 
PreCalc/Trig
Please check the first and help with the secondthank you Find all possible rational roots of f(x) = 2x^4  5x^3 + 8x^2 + 4x+7 1.I took the constant which is 7 and the leading coefficient which is 2 and factored them 7 factored would … 
Algebra II
1)What method(s) would you choose to solve the equation: x2 + 2x  6 = 0 A. Square roots; there is no xterm. B. Quadratic formula, graphing; the equation cannot be factored easily since the numbers are large. C. Factoring; the equation … 
AlgebraB2
A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation y = 0.04x+ 8.3x + 4.3, where x is the horizontal distance, in meters, from the starting point on the roof and y is the … 
Pre Calc
Write an equation to a polynomial function that has the following properties: Fourth degree equation Lead coefficient is 2 Two negative real roots and one positive real root The positive real root has multiplicity of 2 
discret
Determine whether these are valid arguments. a. If x is a positive real number, then x2 is a positive real number. Therefore, if a2 is positive, where a is a real number, then a is a positive real number. b. Ifx2 ≠0,wherexisarealnumber,thenx≠0.Letabearealnumberwitha2 …