Question

Factor out the negative common monomial factor -20x^(2)+5x+15

Answer 1

To factor out the negative common monomial factor -20x^2+5x+15, find the greatest common factor (GCF) of the terms. The factored form is -10x^3 + 5x + 15.

Step-by-step explanation:

To factor out the negative common monomial factor -20x2+5x+15, we need to find the greatest common factor (GCF) of the terms. Here's the step-by-step process:

1. Write down the prime factorization of each coefficient: -20 = -2 * 2 * 5, 5 = 5, 15 = 3 * 5.
2. Identify the common factors among the coefficients: The only common factor is 5.
3. Write down the highest power of x that appears in each term: x2, x, x0.
4. Take the GCF of the coefficients and the highest power of x: -20x2 = -2 * 2 * 5 * x2 = -10x2, 5x = 5 * x = 5x, 15 = 3 * 5 = 15.
5. Combine the GCF with the highest power of x: GCF * highest power of x = (-10x2)x = -10x3.
6. Divide each term in the original expression by the GCF * highest power of x to get the factored form: (-10x3) + (5x) + (15).

Therefore, the factored form of -20x2+5x+15 is -10x3 + 5x + 15.