Factoring is the process of breaking down a mathematical expression into smaller parts or factors. It is the opposite of multiplication.
Factoring allows us to simplify complex expressions and solve equations more easily. It is also useful in finding the roots of quadratic equations and identifying common factors in polynomials.
The general method for factoring a quadratic expression is to find two numbers that multiply to give the constant term, and add up to give the coefficient of the middle term. These numbers will then be used as the factors of the quadratic expression.
When factoring a quadratic expression with a leading coefficient of 2, you can use the "ac method". First, find two numbers that multiply to give the constant term (2 in this case) and add up to give the coefficient of the middle term (a in this case). Then, rewrite the quadratic expression as 2x^2 + (these two numbers)x - 2a - 8. You can then factor this expression using the general method mentioned above.
Yes, you can always check your factoring by expanding the factors and simplifying the expression. If the expanded expression is the same as the original expression, then the factoring is correct.