Question: Factor out the negative common monomial factor with the largest absolute value from the polynomial and then write the polynomial factor in standard form.
6 + 15x - 3x^2
1. **State the problem:** We need to factor out the negative common monomial factor with the largest absolute value from the polynomial $$6 + 15x - 3x^2$$ and then write the resulting polynomial in standard form.
2. **Identify the common factors:** The coefficients are 6, 15, and -3. The greatest common factor (GCF) of their absolute values is $$3$$.
3. **Since we want the negative common factor, we take $$-3$$ as the factor to extract.**
4. **Factor out $$-3$$:**
$$6 + 15x - 3x^2 = -3\left(\frac{6}{-3} + \frac{15x}{-3} - \frac{3x^2}{-3}\right)$$
5. **Simplify inside the parentheses:**
$$= -3\left(-2 - 5x + x^2\right)$$
6. **Rewrite the polynomial inside the parentheses in standard form (descending powers of $$x$$):**
$$= -3\left(x^2 - 5x - 2\right)$$
**Final answer:**
$$6 + 15x - 3x^2 = -3\left(x^2 - 5x - 2\right)$$