Final answer:
To factor the polynomial 12x + 10x² - 16, we can start by factoring out the greatest common factor, which is 2. Then, we can use factoring by grouping to factor the quadratic term into (x + 2)(5x - 4). This is the factored form of the polynomial.
Step-by-step explanation:
To factor the polynomial 12x + 10x² - 16, we need to look for common factors. First, we can factor out the greatest common factor, which is 2:
2(6x + 5x² - 8)
Next, we can rearrange the quadratic term to match the standard form, which is Ax² + Bx + C. So, we have:
2(5x² + 6x - 8)
Now, we need to factor the quadratic term. We can use the method of factoring by grouping to do this. Split the middle term (6x) into two terms that can be factored separately:
2(5x² + 10x - 4x - 8)
Factor out the greatest common factor from the first two terms, and from the last two terms:
2(5x(x + 2) - 4(x + 2))
Now, we can see that (x + 2) is common to both terms, so we can factor it out:
2(x + 2)(5x - 4)
This is the factored form of the polynomial.