SOLUTION: Write a trinomial that has a GCF of 7x to exponent of 2

Question 1201744: Write a trinomial that has a GCF of 7x to exponent of 2
Found 4 solutions by josgarithmetic, greenestamps, ikleyn, math_tutor2020:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
, and you are free to choose any a, b, c which not zero. This is not the only possible way.
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

A GCF is a greatest common factor between two or more expressions.

What does it mean for a single trinomial (or any single polynomial) to have a GCF?

I could make a guess; but I shouldn't have to, and if I'm wrong it would be a waste of time....

Re-post, using correct mathematical language.

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

It is typical " soup of words ".

Each word is some Math term, but taken altogether, they make NONSENSE.

Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Answer: 21x^4 + 28x^3 + 35x^2
Other answers are possible.

Explanation:

Pick any trinomial where the coefficients are relatively prime to one another
This means the GCF of the coefficients is 1.
Let's say we go for 3x^2+4x+5

Multiply that with 7x^2
7x^2(3x^2+4x+5)
7x^2*3x^2 + 7x^2*4x + 7x^2*5 ... distributive property
21x^4 + 28x^3 + 35x^2
This leads to an expression where we are guaranteed to have 7x^2 as the GCF of each term of the trinomial.

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