Question

When we factor this equation the correct answer would be "-2x(7 + 6x)". But why would "2x(-7-6x)" be wrong?

Answer 1

The factorization 2x(-7-6x) is not wrong because distributing the outer 2x to each term inside gets us

• 2x times -7 = -14x
• 2x times -6x = -12x^2

which leads back to -14x-12x^2

Therefore, 2x(-7-6x) = -14x - 12x^2 is true.

Convention usually has us pull out the negative so the terms inside are all positive. This is just a practice done. There technically isn't any right way vs wrong way to factor, when we compare the two different factorizations. I think it's more of a subjective style than anything.

Answer 2

Explanation:

Although it is right,

The rule is that we stop factoring, if we can't factor out a constant that isn't 1.

In your example, we can still factor out-1.