I spend hours trying to factor an equation! I need help trying to factor 2x^2+19x+24

Hours?
(2x+3)(x+8)

Factoring an equation can be a challenging task, but with some practice and using certain techniques, it becomes easier over time. Let's look at the equation 2x^2 + 19x + 24 and go through the steps to factor it.

Step 1: Multiply the coefficient of the term with the highest power of x (in this case, 2) by the constant term (in this case, 24). So, 2 * 24 = 48.

Step 2: Now, we need to find two numbers whose product is 48 and whose sum is the coefficient of the middle term, which is 19 in this case.

To do this, we need to look for two numbers that can multiply to give us 48. In this case, we can try using trial and error, starting with smaller numbers.

The pairs of numbers that multiply to give 48 are: (1, 48), (2, 24), (3, 16), (4, 12), and (6, 8).

Step 3: We need to choose the pair that also adds up to 19. By observing the pairs, we can see that (3, 16) is the pair that adds up to 19, which matches the middle term coefficient.

Step 4: Now, we will split the middle term 19x using the pair (3, 16) as coefficients. We rewrite the original equation as follows:

2x^2 + 3x + 16x + 24

Step 5: Group the terms:

(2x^2 + 3x) + (16x + 24)

Step 6: Factor out the Greatest Common Factor (GCF) from each group:

x(2x + 3) + 8(2x + 3)

Step 7: Notice that both groups have a common factor, (2x + 3). We can now factor it out:

(2x + 3)(x + 8)

And there you have it! The factored form of the equation 2x^2 + 19x + 24 is (2x + 3)(x + 8).

Remember, factoring equations requires practice. Trial and error, along with identifying patterns and common factors, are key skills to develop when factoring equations.