Question

Rozłóż wyrażenia na czynniki:

1. 2x³-2x

2. 36y+12xy+x²y

3. 8yx²-8yx+2y

4. 4x²-40x +100

5. 5x³ -90x²+405x

6. 27x³+18x²+3x

7. 16(x-3)-x²(x-3)

8. x²(2x-1)-3(2x-1)

9. 16(x-3)-x²(x-3)

10. (x+5)x²-(x+5)

Answer 1

1. 2x³-2x = 2x ( x² - 1) = 2x(x - 1)(x + 1)

 

2. 36y+12xy+x²y = y(36 + 12x + x²) = y(6 + x)² = y(6 + x)(6 + x)

 

3. 8yx²-8yx+2y = 2y(4x² - 4x + 1) = 2y(2x - 1)² = 2y(2x - 1)(2x - 1)

 

4. 4x²-40x +100 = (2x - 10)² = (2x - 10)(2x - 10)

 

5. 5x³ -90x²+405x = 5x(x² - 18x + 81) = 5x(x - 9)² = 5x(x - 9)(x - 9)

 

6. 27x³+18x²+3x = 3x(9x² + 6x + 1) = 3x(3x + 1)² = 3x(3x + 1)(3x + 1)

 

7. 16(x-3)-x²(x-3) = (x - 3)(16 - x²) = (x - 3)(4 - x)(4 + x)

 

8. x²(2x-1)-3(2x-1) = (2x - 1)(x² - 3) = (2x - 1)(x - √3)(x + √3)

 

9. 16(x-3)-x²(x-3) = (x - 3)(16 - x²) = (x - 3)(4 - x)(4 + x)

 

10. (x+5)x²-(x+5) = (x + 5)(x² - 1) = (x + 5)(x - 1)(x + 1)