factor

1. 4th Degree Polynomial

How to factor this function? y = x^4 + x^2 + 2
2. Prove that a binomial is a factor

Hi, I hope someone can help. I'm suppose to prove that x + a is a factor of (x + a)^5 + (x - c)^5 + (a - c)^5. The textbook solution is if f(x) = (x + a)^5 + (x - c)^5 + (a - c)^5, then f(-a) = 0. I don't totally understand this solution, so could someone please elaborate on this? Best, Olivia
3. Proving a factor of a polynomial

Hi, I hope someone can help provide elaboration on the homework question that I'm faced with, and why the solution is what it is. The homework question is as follows: Determine a general rules to help decide whether x - a and x + a are factors of x^n - a^n and x^n + a^n. The homework...
4. Finding the perfect cube

Hi, Can someone please explain the thinking involved to realize that y =-x^4-15x^3-75x^2-125x can be factored into y = -x(x+5)^3? I know that when I expand y = -x(x+5)^3 it results to y =-x^4-15x^3-75x^2-125x, but I can't think in the reverse way. Best, Olivia
5. I have many questions.

First of all, backstory: I am taking an Intermediate Algebra class, and needless to say, it's kicking my arse. So, that being said, I think I'm going to ask a few questions. What would I do to solve this one? Note: I have never learned how to factor. Factor completely: -6r3s + 8r2s2 - 10rs...
6. factorising so that one factor must be:

I just started a chapter on factorising and for the life of me can't figure the following out: Factorise 1 + x^2 so that one factor must be: 1. 1/x 2. x 3. x^2 I've attached how the examples mentioned above are solved. Is this the best possible explanation for solving the above mentioned or...
7. Factor out the GCF of the three terms, then complete the factorization

Ok, I don't even kind of understand this problem... Please help! (Cool) Factor out the GCF of the three terms, then complete the factorization of x4+9x3+14x2.
8. Why do you force factor out on X to find the Horizontal Asymptote?

I understand that if the exponents of the leading coefficients are the same, then the HA is just those leading coefficients divided. But i've been told that the true way to find it is by force factoring out an x, and plugging in x as it approaches infinite. Can someone explain why?
9. Zero divisors of a polynomial factor ring

Problem As we've observed, a(x) = x^2 + x + 1 2 Z_3[x] is reducible. According to the theory (Theorem 17.5), Z3[x]=(a(x)) is not a field. Find a non-0 element q(x)+(a(x)) that has no inverse. Suggestion: Find a 0-divisor of Z3[x]=(a(x)). Attempt at a solution: I've factored x^2 + x + 1 into...
10. integrating factor

is my integral R(x) and R(y) correct ? why it look so complicated ?
11. Principal factor analysis

Hello everyone: I have a statistical problem I've been trying to solve for quite a while without any success. I'm not sure if I am right here for my question but maybe someone can help me. I want to recreate a measure for earnings smoothing used in literature but I don't fully understand how...
12. Use the given roots to factor.

5x^5-2x^4-62x^3+82x^2-67x+84 x=i,3 I know the highest degree polynomial determines how many possible roots it has. So possible is 5. also answer is: (5x-7)(x-3)(x+4)(x-i)(x+i)
13. Can someone help me with a few problems... having some trouble

Hi if someone could help me with the following questions that would be great! (with work) 1.Find the roots of the following equations a) 0=x^4 - 8x^2 + 16 b) 2x= 4x^3 - 2x^2 2. Find all of the zeroes in the following P(x)= x^4 - 4x^3 - 16x^2 + 21x + 18 3. Is (x+2) a factor of x^3 - 3x^2 -...
14. Factor of Resistance

The resistance y in ohms of 1000 feet of solid copper wire at 77°F can be approximated by the mathematical model y = [(10, 000)/(x^2)] - 0.37, where x lies in the interval [5, 100]. Keep in mind that x is the diameter of the wire in mils (0.001 inches). If the diameter of the wire is...
15. factor theorem and remainder theorem

Hi; Can someone tell me the difference between the factor theorem and the remainder theorem in polynomials? I know the remainder theorem but can't see a difference in the factor theorem. Thanks.
16. Give the starting value a, the growth factor for the given exponential function

Q = 13 * 2(t/10)-1 has: a = b = Q = (1/7)*(cubed root of 8t) has: a= b= Q(t) = 0.0033(2.26)-4t The initial value is a = The growth factor is b= The growth rate is r = I'm at a loss as to how to solve these problems. Do I need to get it to abt form?
17. Factor x^12 - 2500

Factor x^12 - 2500
18. Factor x^8 - 625

Factor x^8 - 625
19. An exponential function with a growth factor between 0 and 1

1. An exponential function with a growth factor between 0 and 1 A. is decreasing B. is constant C. is increasing D. sometimes decreases and sometimes increases 2. An exponential function with a growth factor greater than 1 A. is decreasing B. is constant C. is increasing D...
20. Factor x^4 + 64

Factor CompletelyI found this solution online.I want to know where 16x^2 comes from.　 x^⁴ + 64 = (x^⁴ + 16x^²+ 64) - 16x^² = (x^² + 8)^² - (4x)^² = (x^² - 4x + 8)(x^² + 4x + 8)