Can you factor these for me?

12x^3 + 6x^2 - 3x - 2
2x^2 +x - 6
25 - 4(x^2 - )^2
y^2 - 3y - 10
(3x - 1)^2 -36
x^3 - 3x^2 - 16x + 48
4x^2 + 7x +3
6x^2 - 19x + 15
5x^4 - 45x^2

I could, but you haven't shown that you've put any effort into doing so yourself.

Also, your third homework question you want someone to do for you is missing a term.

Sure! Let's factor each of the given expressions step by step:

1. 12x^3 + 6x^2 - 3x - 2:

To factor this expression, we can use the technique of grouping.
First, group the terms with common factors:
(12x^3 + 6x^2) + (-3x - 2)

Now factor out the greatest common factor from each group:
6x^2(2x + 1) - 1(3x + 2)

Combine the factored terms:
6x^2(2x + 1) - (3x + 2)

The factored form of the expression is: (2x + 1)(6x^2 - 3x - 2)

2. 2x^2 + x - 6:

This expression is a trinomial, which can be factored using the technique of factoring by grouping or the quadratic formula.
However, in this case, we can use the fact that the coefficients multiply to the constant term and add up to the coefficient of the middle term (2 * -6 = -12 and 1 + (-6) = -5).
We can factor this expression directly using the product-sum method:

Split the middle term (-1x) into two terms by finding two numbers that multiply to -12 and add up to -1 (the coefficient of the middle term):
-3 and 4 satisfy these conditions (-3 * 4 = -12 and -3 + 4 = -1).

Rewrite the trinomial using these numbers:
2x^2 - 3x + 4x - 6

Group the terms:
(2x^2 - 3x) + (4x - 6)

Now factor out the greatest common factor from each group:
x(2x - 3) + 2(2x - 3)

Combine the factored terms:
(x + 2)(2x - 3)

The factored form of the expression is: (x + 2)(2x - 3)

3. 25 - 4(x^2 - )^2:

The given expression is missing a term inside the parenthesis. Please provide the missing term, and I will be happy to help you factor it.

4. y^2 - 3y - 10:

This is a quadratic trinomial that can be factored using the product-sum method or the quadratic formula. In this case, the factors of the constant term (-10) that add up to the coefficient of the middle term (-3) are -5 and 2.

Rewrite the trinomial using these factors:
y^2 - 5y + 2y - 10

Group the terms:
(y^2 - 5y) + (2y - 10)

Now factor out the greatest common factor from each group:
y(y - 5) + 2(y - 5)

Combine the factored terms:
(y + 2)(y - 5)

The factored form of the expression is: (y + 2)(y - 5)

5. (3x - 1)^2 - 36:

This expression is a binomial squared, which can be factored using the difference of squares formula.
The difference of squares formula states that a^2 - b^2 can be factored as (a + b)(a - b).

In this case, a = (3x - 1) and b = 6.

Apply the difference of squares formula:
[(3x - 1) + 6][(3x - 1) - 6]

Combine like terms:
(3x + 5)(3x - 7)

The factored form of the expression is: (3x + 5)(3x - 7)

6. x^3 - 3x^2 - 16x + 48:

To factor this cubic expression, we need to find its rational roots.
We can use the rational root theorem or synthetic division to find the possible roots, then use long division or synthetic division to divide the expression by the roots to find the remaining factors.

Since there are no rational roots in this case, the expression cannot be factored further over the set of rational numbers.

7. 4x^2 + 7x + 3:

This is a quadratic trinomial. To factor it, we can use the product-sum method or quadratic formula. However, in this case, we can find two numbers that multiply to 12 (the product of the coefficient of x^2 and the constant term) and add up to 7 (the coefficient of the middle term). The numbers are 3 and 4.

Rewrite the trinomial using these factors:
4x^2 + 3x + 4x + 3

Group the terms:
(4x^2 + 3x) + (4x + 3)

Now factor out the greatest common factor from each group:
x(4x + 3) + 1(4x + 3)

Combine the factored terms:
(x + 1)(4x + 3)

The factored form of the expression is: (x + 1)(4x + 3)

8. 6x^2 - 19x + 15:

To factor this quadratic trinomial, we can use the product-sum method or the quadratic formula.
In this case, the factors of 15 (the constant term) that add up to -19 (the coefficient of the middle term) are -15 and -1.

Rewrite the trinomial using these factors:
6x^2 - 15x - 4x + 15

Group the terms:
(6x^2 - 15x) + (-4x + 15)

Now factor out the greatest common factor from each group:
3x(2x - 5) - 3(2x - 5)

Combine the factored terms:
(3x - 3)(2x - 5)

The factored form of the expression is: (3x - 3)(2x - 5)

9. 5x^4 - 45x^2:

This expression has a common factor of x^2.
We can factor it out, leaving the remaining factors inside the brackets:

x^2(5x^2 - 45)
x^2(5(x^2 - 9))

The expression inside the brackets is a difference of squares. We can factor it using the difference of squares formula:

x^2(5(x - 3)(x + 3))

The factored form of the expression is: x^2(5x - 15)(x + 3)

Please double-check the answers to ensure accuracy, as human error may occur during the factoring process.