SOLUTION: Let a, b, c, and dbe positive integers such that a < b < c < d.Suppose b = a + 2, c = a + 4, and d = a + 5. Write x^a + x^b + x^c + x^d in factored form.

Question 513466: Let a, b, c, and dbe positive integers such that a < b < c < d.Suppose b = a + 2, c = a + 4, and d = a + 5. Write x^a + x^b + x^c + x^d in factored form.
Answer by drcole(72) (Show Source): You can put this solution on YOUR website!
First, let's substitute in for b, c, and d, since we are given formulae for all three in terms of a:

Now let's remember how exponents add:

for all p and q. Thus we can rewrite our expression as:

Now let's look for ways to factor our expression. Notice that x^a is a common factor in each term, so we'll factor x^a out:

There doesn't appear to be any way to easily factor the remaining polynomial (the only possibilities for rational roots are 1 and -1, and neither of these work), so it looks like we're done.
RELATED QUESTIONS
suppose that a,b,c and d are positive numbers such that a/b < c/d show that a/b <... (answered by richard1234)

let. a, b, c, d be positive integers and (log( b)/log (a))=3/2 ,(log (d)/log (c))=5/4 (answered by Edwin McCravy)

A, B, C and D are positive integers such that A^2 + 3B^2 + 3C^2 + 5D^5 = 1002. What is... (answered by ikleyn)

Suppose a,b,c,d are positive integers with a <= c <= d and c/d <= a/b. Prove that (a-b)... (answered by lynnlo)

Suppose a, b, c, d are positive integers with a ≤ c ≤ d and c/d ≤ a/b.... (answered by lynnlo)

Let a, b, c, d be positive integers such that loga(b)=3/2 and logc(d) =5/4. If a −... (answered by ankor@dixie-net.com)

a(x+b)-c=d (answered by Alan3354)

Let f(x) =x^n + a(sub1)x^n-1 + a(sub2)x^n-2..........a(sub n-1)x+a(sub n) be a polynomial (answered by khwang)

a|bx-c|=d Solve for x. Assume that a, b, c, and d represent positive real... (answered by stanbon)