Question

How do I factor the polynomial 3x^2 - 2x - 5 using the 7-step grouping method?

Answer 1

To factor the polynomial 3x^2 - 2x - 5 using the 7-step grouping method, split the middle term, group the terms, and factor out the GCF to get the factored form (x - 1)(3x - 5).

Step-by-step explanation:

To factor the polynomial 3x^2 - 2x - 5 using the 7-step grouping method:

1. Split the middle term -2x into two terms so that their product is equal to the product of the coefficient of the quadratic term (3) and the constant term (-5). In this case, the terms are -5x and 3x.
2. Group the four terms into pairs: (3x^2 - 5x) and (-2x - 5).
3. Factor out the greatest common factor (GCF) from each pair: x(3x - 5) - 1(2x + 5).
4. Next, factor out the GCF from each group. The factors of (3x - 5) will be the same in both groups, so we can factor it out. The new expression becomes: (x - 1)(3x - 5).

Therefore, the factored form of the polynomial 3x^2 - 2x - 5 is (x - 1)(3x - 5).