Question

Write a trinomial of degree 4 such that the GCF of its terms is one ???

Answer 1

@annas

Answer 2

Help???

Answer 3

Here you can learn a thing or two about Greatest Common Factor. http://www.mathsisfun.com/greatest-common-factor.html
In this case they ask you write a trinomial (polynomial with 3 terms) of dregree 4 such that de greatest common factor of it's terms is 1, in other words, the terms must not share eny factors.
An easy way to do this is by using only prime numbers (numbers that are only divisible by 1 and themselves) for the terms, because they are axactly divided by number 1 only. So, as long as you choose different primes for the terms, you will have solved the problem!
The first primes are: 1,2,3,5,7,11,13,...
And an example solution would be: T(x)=1*x^4+2*x^3+3*x^2

Answer 4

I dont understand

Answer 5

When you divide two natural numbers, say A/B (naturals are 1, 2, 3, 4, etc..), you have two possible outcomes. Either you get as a result another natural number (call it "C"), or you get as a result a rational number (rational numbers are fractions or numbers with finite or repiting decimals).
For the case when A/B results in a natural number C (for example, 6/2=3), number B receives the name of "Divisor of number A", or "FACTOR OF A".
Some numbers have more factors than others, here I show you some examples:

Factors of 8: 1, 2, 4, 8
(8/1=8, 8/2=4, 8/4=2, 8/8=1)

Factors of 12: 1, 2, 3, 4, 6, 12
(12/1=12, 12/2=6, 12/3=4, 12/4=3, 12/6=2, 12/12=1)

Factors of 16: 1, 2, 4, 8, 16
(16/1=16, 16/2=8, 16/4=4, 16/8=2, 16/16=1)

Now, do these three numbers (8, 12, and 16) have any factors in COMMON? Yes! They ALL share the factors 2 and 4.
And finally, among the common factors, which one is the greatest? Well, the Greatest Common Factor (GCF) of the list (8, 12, 16) is the number 4.

What you need to do in the excercise is to make up a trinomial of degree 4 such that the Greatest Common Factor of it's terms is 1.
A trinomial looks like this:
Trin(x)=A*x^d+B*x^f+C*x^g
The degree of the trinomial is determined by the higest power, if you want it to be degree 4, you should use that power and any two other lower powers, for example:
Trin(x)=A*x^4+B*x^2*C*x^1
You can interpret A, B and C as the "terms" of the trinomial, although this is not technically correct, it will help understanding what we are doing.
That is, you must pick any three numbers (A, B and C) such that their Greatest Common Factor is 1. Of course, the easiest solution is setting A, B and C equal to 1. Because the only factor of 1 is itself (1), so there is only one factor that A, B and C share, and that factor is the number 1, so the Greatest Common Factor of the list (A=1, B=1 and C=1) is 1.
And the easiest solution is:
Trin(x)=1*x^4+1*x^2+1*x
Which simplifies to
Trin(x)=x^4+x^2+x

I hope that turns out helpful!