help on this please?
Factor completely 2x2 - 2x - 24.
(2x - 6)(x + 4)
(2x - 8)(x + 3)
2(x - 3)(x + 4)
2(x - 4)(x + 3)
2x^2-2x-24
2(x^2-x-12)
2(x-4)(x+3)
thanks alot
To factor the quadratic expression 2x^2 - 2x - 24 completely, we need to find two binomial expressions that multiply together to give us the original expression. Here's how you can do it:
Step 1: Look for common factors among the coefficients (numbers in front of x^2, x, and the constant term). In this case, the common factor is 2. We can factor out 2 from all the terms, giving us:
2(x^2 - x - 12)
Step 2: Now, we need to factor the trinomial expression x^2 - x - 12. To do this, we need to find two numbers whose product is equal to the constant term (-12) and whose sum is equal to the coefficient of the x term (-1).
The pairs of numbers that satisfy these conditions are (-4, 3) and (4, -3). Since the coefficient of the x term is negative, we choose the pair that has the same sign as the coefficient of the x term. In this case, the pair is (-4, 3).
Step 3: Rewrite the expression using the factored form. We replace the x term with the sum of the two numbers we found in step 2, and we write the expression as the product of two binomials.
The factored form of x^2 - x - 12 is (x - 4)(x + 3).
Step 4: Rewrite the expression factored in step 3, but now include the 2 that we factored out in step 1:
2(x - 4)(x + 3)
Therefore, the correct answer is: 2(x - 4)(x + 3).