factoring completely with solution
1. x²+5x+6
2. x²-8x+15
3. x²-6x+8
4. x²+8x+12 5. x²-6x+8
6. x²+10x-11
7. x²-3x-40
8. x²-3x-28
9. 2x²+2x-24
10. 5x²-5x-100
11. 5x²y-30xy²+40y³
12. -4x²y+16xy²-12y³
13. (3x-2)²-2(3x-2)-35
14. (2x-5)²+6(2x-5)+5
15. 2x²+7x+6
16. 2x²+8x+8
17. 3x²-10x+3
18. 3x²-30x+75
19.3x²+14x-15
20. 5x²+8x-4
21. 6x²-5x-6
22. 6x²-41x-7
23. 15x²+17x-4
24. 35x²+13x-12
25. 8x³+14x²+5x
26. x²-64
27. x²-100
28. 49y²-25x²
29.81b²-36
30. (3x+y)²-9
31. (4a+b)²-25c²
32. (2x-3)²-(3x+2)²
33. (5x-6)²-(4x-3)²
34. y⁴-y²-72
35. y⁴-5y²+4
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Verified answer
Answer:
Solution
Step-by-step explanation:
Let's factor each of the given expressions completely:
1. x² + 5x + 6
Factored: (x + 2)(x + 3)
2. x² - 8x + 15
Factored: (x - 3)(x - 5)
3. x² - 6x + 8
Factored: (x - 2)(x - 4)
4. x² + 8x + 12
Factored: (x + 2)(x + 6)
5. x² - 6x + 8
Factored: (x - 2)(x - 4)
6. x² + 10x - 11
Factored: (x + 11)(x - 1)
7. x² - 3x - 40
Factored: (x - 8)(x + 5)
8. x² - 3x - 28
Factored: (x - 7)(x + 4)
9. 2x² + 2x - 24
Factored: 2(x + 6)(x - 2)
10. 5x² - 5x - 100
Factored: 5(x + 4)(x - 5)
11. 5x²y - 30xy² + 40y³
Factored: 5y(x - 2)(x - 4)(x + 2)
12. -4x²y + 16xy² - 12y³
Factored: -4y(x - 2)(x - 3)(x + 3)
13. (3x - 2)² - 2(3x - 2) - 35
Factored: (3x - 2 - 7)(3x - 2 + 5)
Simplified: (3x - 9)(3x + 3)
14. (2x - 5)² + 6(2x - 5) + 5
Factored: (2x - 5 + 1)(2x - 5 + 5)
Simplified: (2x - 4)(2x)
15. 2x² + 7x + 6
Factored: (2x + 3)(x + 2)
16. 2x² + 8x + 8
Factored: 2(x + 2)(x + 2)
17. 3x² - 10x + 3
Factored: (3x - 1)(x - 3)
18. 3x² - 30x + 75
Factored: 3(x - 5)(x - 5)
19. 3x² + 14x - 15
Factored: (3x - 1)(x + 15)
20. 5x² + 8x - 4
Factored: (5x - 2)(x + 2)
21. 6x² - 5x - 6
Factored: (3x - 2)(2x + 3)
22. 6x² - 41x - 7
Factored: (3x + 1)(2x - 7)
23. 15x² + 17x - 4
Factored: (3x - 1)(5x + 4)
24. 35x² + 13x - 12
Factored: (7x - 3)(5x + 4)
25. 8x³ + 14x² + 5x
Factored: x(2x + 1)(4x + 5)
26. x² - 64
Factored: (x + 8)(x - 8)
27. x² - 100
Factored: (x + 10)(x - 10)
28. 49y² - 25x²
Factored: (7y + 5x)(7y - 5x)
29. 81b² - 36
Factored: 9(9b + 6)(9b - 6)
30. (3x + y)² - 9
Factored: (3x + y + 3)(3x + y - 3)
31. (4a + b)² - 25c²
Factored: (4a + b + 5c)(4a + b - 5c)
32. (2x - 3)² - (3x + 2)²
Factored: (2x - 3 + 3x + 2)(2x - 3 - 3x - 2)
Simplified: (5x - 1)(-x - 5)
33. (5x - 6)² - (4x - 3)²
Factored: (5x - 6 + 4x - 3)(5x - 6 - 4x + 3)
Simplified: (9x - 9)(x - 3)
34. y⁴ - y² - 72
Factored: (y² - 9)(y² + 8)
Further Factored: (y - 3)(y + 3)(y² + 8)
35. y⁴ - 5y² + 4
Factored: (y² - 4)(y² - 1)
Further Factored: (y - 2)(y + 2)(y - 1)(y + 1)
These are the completely factored forms of the given expressions.