Chapter 8.4, Problem 27MCQ

To determine

To find: A trinomial that has $9x^2$ as the GCF of its terms.

Answer to Problem 27MCQ

  $18x^4+9x^3+27x^2$

Explanation of Solution

Given information: The trinomial has $9x^2$ as the GCF of its terms.

Calculation:

A trinomial is a polynomial with 3 terms.

Let the trinomial be $18x^4+9x^3+27x^2$ .

The prime factorization of the terms of the polynomial is,

  $\begin{array}{l}18x^4=3\cdot 3\cdot 2\cdot x\cdot x\cdot x\cdot x\\ 9x^3=3\cdot 3\cdot x\cdot x\cdot x\\ 27x^2=3\cdot 3\cdot 3\cdot x\cdot x\end{array}$

Thus, the GCF of the terms of the polynomial is $3\cdot 3\cdot x\cdot x\text{ or }9x^2$ .

Hence, $18x^4+9x^3+27x^2$ is a trinomial that has $9x^2$ as the GCF of its terms.