Factor completely 2x² + 2x - 24
2(x - 3)(x + 4), (2x - 6)(x + 4), (2x - 3)(x + 8), 2(x - 4)(x + 6)

Solution:

Given is a quadratic polynomial.

Step 1: 2x² + 2x - 24 can be written as 2 (x² + x -12) = 0. (taking the GCD out)

Let us factorize the polynomial to find the value of x by splitting the middle term.

Step 2: Identify the values of a, b and c.

In the above equation, a is coefficient of x² = 1,

b is the coefficient of x = 1

and c is the constant term = -12.

Step 3: Multiply a and c and find the factors that add up to b.

1 × (-12) = -12

⇒ -3 and 4 are the factors of -12 that add up to b.

Step 4: Split bx into two terms.

2 (x² + 4x - 3x -12)

Step 5: Take out the common factors by grouping.

2[x(x + 4) - 3(x +4)] 

2(x + 4) (x - 3)

Thus 2x² + 2x - 24 is factorized as 2(x + 4) (x - 3)

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Factor completely 2x² + 2x - 24
2(x - 3)(x + 4), (2x - 6)(x + 4), (2x - 3)(x + 8), 2(x - 4)(x + 6)

Summary:

The factor of the equation 2x² + 2x - 24 is 2(x + 4)(x - 3) or 2(x - 3)(x + 4)