What is the factored form of the polynomial 3X² + 10X - 8?

• A. (3X - 2)(X + 4)
• B. (3X + 2)(X - 4)
• C. (3X + 2)(X + 4)
• D. (3X - 4)(X + 2)

Answer: (A)

To factor the polynomial 3X² + 10X - 8, we look for two numbers that multiply to the product of the coefficient of X² (which is 3) and the constant term (which is -8). The product is 3 * -8 = -24. Additionally, we need these two numbers to add up to the coefficient of the X term, which is 10.

The numbers that satisfy these conditions are 12 and -2, since 12 * -2 = -24 and 12 + (-2) = 10. With these numbers, we can rewrite the middle term of the polynomial:

3X² + 12X - 2X - 8

Next, we group the terms in pairs:

(3X² + 12X) + (-2X - 8)

From the first group, we can factor out 3X:

3X(X + 4)

From the second group, we factor out -2:

-2(X + 4)

Now we can combine the two groups:

3X(X + 4) - 2(X + 4)

Since both terms contain a common factor of (X + 4), we can factor that