write a trinomial of degree 4 such that the GCF of its terms is 1
2x^4 - 5x + 7
2x^4-5x+7
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To write a trinomial of degree 4 such that the greatest common factor (GCF) of its terms is 1, we'll need to choose our terms carefully.
First, let's start by understanding what a GCF is. The GCF is the largest number that divides evenly into all terms of an expression. In this case, since we're looking for a trinomial, we'll have three terms.
To ensure that the GCF of our trinomial is 1, we need to make sure that there are no common factors among the terms. Let's break down the factors of a trinomial of degree 4.
A trinomial of degree 4 typically has the form: ax^4 + bx^2 + c, where a, b, and c are coefficients.
To avoid a common factor, we'll make sure that a = 1, since the GCF of the trinomial should also be 1.
So, a trinomial of degree 4 with a GCF of 1 could be written as x^4 + bx^2 + c.
Now, we'll need to choose the values of b and c. To ensure that the GCF of the trinomial is 1, we'll need to select values that have no common factors.
Let's take b = 3 and c = 7 as an example.
Therefore, the trinomial would be: x^4 + 3x^2 + 7.
In this case, the GCF of the trinomial's terms is 1 because there are no common factors among 1, 3, and 7.