Chapter 8.4, Problem 28MCQ

To determine

To find: A trinomial of degree 4 such that the GCF of its terms is 1.

Answer to Problem 28MCQ

  $x^4+9x^2+5$

Explanation of Solution

Given information: The trinomial is of degree 4 and GCF of its terms is 1.

Calculation:

A trinomial of degree 4 is a polynomial with 3 terms whose highest degree is 4.

A trinomial of degree 4 is $x^4+9x^2+5$ .

The prime factorization of the terms of the polynomial is,

  $\begin{array}{l}{x}^4=x\cdot x\cdot x\cdot x\\ 9x^2=3\cdot 3\cdot x\cdot x\\ 5=5\end{array}$

Thus, the GCF of the terms of the polynomial is 1.

Hence, $x^4+9x^2+5$ is a trinomial of degree 4 such that the GCF of its terms is 1.