Factor these expressions:

3x^2 + 8x + 4

2x^2 - 7x + 6

5x - 2x^2 - 3

1. 3x^2 + 8x + 4

3x^2 + (2x+6x) + 4
(3x^2+6x) + (2x+4)
3x(x+2) + 2(x+2)
(x+2)(3x+2).

2. 2x^2 - 7x + 6

Use the AC method:
A*C = 2*6 = 12 = -2*-6 = -3*-4
Use -3 and -4 for factoring, because their sum = B(-7).
2x^2 + (-3x-4x) + 6
Arrange the 4 terms to form 2 factorable
pairs:
(2x^2-3x) + (-4x+6)
x(2x-3) + -2(2x-3)
(2x-3)(x-2).

3. Use same procedure.

Po5t it.

To factor these expressions, we first need to look for common factors, if any. Then, we'll try to break down each expression into two binomial factors.

Let's start with the first expression, 3x^2 + 8x + 4.
Step 1: Look for common factors (if any) among the coefficients. In this case, there are no common factors among 3, 8, and 4.
Step 2: Multiply the coefficient of x^2 (3) with the constant term (4). The product is 12.
Step 3: Find two numbers that multiply to give 12 (the product from step 2) and add up to the coefficient of x (8). The numbers in this case are 6 and 2 since 6 * 2 = 12 and 6 + 2 = 8.
Step 4: Rewrite the original expression using the numbers found in step 3. We get: 3x^2 + 6x + 2x + 4.
Step 5: Group the terms. (3x^2 + 6x) + (2x + 4).
Step 6: Factor out the common factors from each group. We can factor out 3x from the first group and 2 from the second group: 3x(x + 2) + 2(x + 2).
Step 7: Notice that we have a common factor of (x + 2) in both terms. We can factor that out: (3x + 2)(x + 2).

Next, let's factor the second expression, 2x^2 - 7x + 6.
Step 1: Look for common factors among the coefficients. There are no common factors between 2, -7, and 6.
Step 2: Multiply the coefficient of x^2 (2) with the constant term (6). The product is 12.
Step 3: Find two numbers that multiply to give 12, the product from step 2, and add up to the coefficient of x (-7). The numbers in this case are -3 and -4 since -3 * -4 = 12 and -3 + -4 = -7.
Step 4: Rewrite the original expression using the numbers found in step 3. We get: 2x^2 - 3x - 4x + 6.
Step 5: Group the terms. (2x^2 - 3x) + (-4x + 6).
Step 6: Factor out the common factors from each group. We can factor out x from the first group and -2 from the second group: x(2x - 3) - 2(2x - 3).
Step 7: Notice that we have a common factor of (2x - 3) in both terms. We can factor that out: (x - 2)(2x - 3).

Lastly, let's factor the third expression, 5x - 2x^2 - 3.
Step 1: Look for common factors among the coefficients. There are no common factors between 5, -2, and -3.
Step 2: Rearrange the terms so that the quadratic term (2x^2) is in the correct order. We get: -2x^2 + 5x - 3.
Step 3: Multiply the coefficient of x^2 (-2) with the constant term (-3). The product is 6.
Step 4: Find two numbers that multiply to give 6 (the product from step 3) and add up to the coefficient of x (5). The numbers in this case are 6 and 1 since 6 * 1 = 6 and 6 + 1 = 5.
Step 5: Rewrite the original expression using the numbers found in step 4. We get: -2x^2 + 6x - x - 3.
Step 6: Group the terms. (-2x^2 + 6x) + (-x - 3).
Step 7: Factor out the common factors from each group. We can factor out 2x from the first group and -1 from the second group: 2x(-x + 3) - 1(-x + 3).
Step 8: Notice that we have a common factor of (-x + 3) in both terms. We can factor that out: (2x - 1)(-x + 3).
Since (-x + 3) is a common factor, we can also rewrite the final factorization as (2x - 1)(3 - x).

Therefore, the factored forms of the given expressions are:
3x^2 + 8x + 4 = (3x + 2)(x + 2)
2x^2 - 7x + 6 = (x - 2)(2x - 3)
5x - 2x^2 - 3 = (2x - 1)(3 - x) or (2x - 1)(-x + 3)