What is the greatest common factor of the terms of the polynomial?15x4 – 18x3 + 12x2A.2x3B.3x2C.2x2D.3x3

1. Break Down the Problem

We need to find the greatest common factor (GCF) of the terms of the polynomial $15x^4 - 18x^3 + 12x^2$.

2. Relevant Concepts

To find the GCF of a polynomial:

• Identify the coefficients of each term.
• Determine the GCF of these coefficients.
• Identify the lowest power of $x$ present in each term.

3. Analysis and Detail

• The coefficients of the terms:

  • $15$ from $15x^4$
  • $-18$ from $-18x^3$
  • $12$ from $12x^2$

• Finding the GCF of the coefficients $15$, $18$, and $12$:

  • The prime factorization of $15 = 3 \times 5$
  • The prime factorization of $18 = 2 \times 3^2$
  • The prime factorization of $12 = 2^2 \times 3$

  The common prime factors are $3$.

  • The GCF of the coefficients is $3$.

• For the variable $x$:

  • The lowest power of $x$ across the terms is $x^2$.

Thus, the GCF of the polynomial is: $3x^2$

4. Verify and Summarize

The greatest common factor of all terms in the polynomial is confirmed to be $3x^2$.

Final Answer

The greatest common factor of the terms of the polynomial is $3x^2$ (Option B).