factor

How to factor this function? y = x^4 + x^2 + 2

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

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...

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

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...

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...

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.

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?

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...

is my integral R(x) and R(y) correct ? why it look so complicated ?

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...

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)

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 -...

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...

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.

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?

Factor x^12 - 2500

Factor x^8 - 625

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...

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)