Question

Factor each expression.
5.9x^2-4
6. 25x^2-49
7. 144x^2 - 1
8.64x^2 - 25
9. 49x^2 - 16
10. 36x^2 - 49
11.81x^2 - 16
12. 16x^2- 121
13.25x^2- 144
14. 16x^2 - 9
15. x^2-81
16. 4x^2-49

Answer 1

Let's factor each expression step-by-step.

### 5. \(5.9x^2 - 4\)
This is not a standard form for a difference of squares. We can factor out a common factor:
\[
5.9x^2 - 4 = (5.9x^2 - \frac{4}{5.9}) = 5.9(x^2 - \frac{4}{5.9}) = 5.9(x - \sqrt{\frac{4}{5.9}})(x + \sqrt{\frac{4}{5.9}})
\]
However, we'll leave it as is for practical purposes since \(5.9\) is not a perfect square. The next option is to approximate the root and factor if feasible.

### 6. \(25x^2 - 49\)
This is a difference of squares:
\[
25x^2 - 49 = (5x - 7)(5x + 7)
\]

### 7. \(144x^2 - 1\)
Also a difference of squares:
\[
144x^2 - 1 = (12x - 1)(12x + 1)
\]

### 8. \(64x^2 - 25\)
Another difference of squares:
\[
64x^2 - 25 = (8x - 5)(8x + 5)
\]

### 9. \(49x^2 - 16\)
This too is a difference of squares:
\[
49x^2 - 16 = (7x - 4)(7x + 4)
\]

### 10. \(36x^2 - 49\)
Again a difference of squares:
\[
36x^2 - 49 = (6x - 7)(6x + 7)
\]

### 11. \(81x^2 - 16\)
This is a difference of squares:
\[
81x^2 - 16 = (9x - 4)(9x + 4)
\]

### 12. \(16x^2 - 121\)
This is a difference of squares:
\[
16x^2 - 121 = (4x - 11)(4x + 11)
\]

### 13. \(25x^2 - 144\)
This is a difference of squares:
\[
25x^2 - 144 = (5x - 12)(5x + 12)
\]

### 14. \(16x^2 - 9\)
Again, a difference of squares:
\[
16x^2 - 9 = (4x - 3)(4x + 3)
\]

### 15. \(x^2 - 81\)
This is a difference of squares:
\[
x^2 - 81 = (x - 9)(x + 9)
\]

### 16. \(4x^2 - 49\)
This is also a difference of squares:
\[
4x^2 - 49 = (2x - 7)(2x + 7)
\]

### Summary of Factored Forms:
1. \(5.9x^2 - 4\) (needs further simplification or numerical approximation)
2. \(25x^2 - 49 = (5x - 7)(5x + 7)\)
3. \(144x^2 - 1 = (12x - 1)(12x + 1)\)
4. \(64x^2 - 25 = (8x - 5)(8x + 5)\)
5. \(49x^2 - 16 = (7x - 4)(7x + 4)\)
6. \(36x^2 - 49 = (6x - 7)(6x + 7)\)
7. \(81x^2 - 16 = (9x - 4)(9x + 4)\)
8. \(16x^2 - 121 = (4x - 11)(4x + 11)\)
9. \(25x^2 - 144 = (5x - 12)(5x + 12)\)
10. \(16x^2 - 9 = (4x - 3)(4x + 3)\)
11. \(x^2 - 81 = (x - 9)(x + 9)\)
12. \(4x^2 - 49 = (2x - 7)(2x + 7)\)

If you have more questions or need further assistance, feel free to ask!