Answer:
3x² (2x² + 4x + 5)
Explanation:
Step 1: Identify the coefficients.
In the given expression, the coefficients are 6, 12, and 15.
Step 2: Find the GCMF of the coefficients.
The GCMF is the largest number that can divide each coefficient evenly. In this case, the GCMF of 6, 12, and 15 is 3.
Step 3: Identify the variables.
The variables in the expression are x^4, x^3, and x^2.
Step 4: Find the GCMF of the variables.
The GCMF of the variables is the highest power of x that appears in each term. Here, it is x^2.
Step 5: Combine the GCMF of the coefficients and variables.
The GCMF of the coefficients (3) and the GCMF of the variables (x^2) can be multiplied together to get the overall GCMF: 3x^2.
Step 6: Factor out the GCMF from the expression.
To factor out the GCMF 3x^2, divide each term of the expression by 3x^2:
(6x^4 + 12x^3 + 15x^2) / (3x^2) = 2x^2 + 4x + 5
Step 7: Write the factored form.
The factored form of 6x^4 + 12x^3 + 15x^2 is 3x^2(2x^2 + 4x + 5).