13) 3x³ - 14x² + 4x + 3
= 3x³ + x² - 15x² - 5x + 9x + 3
= (3x³ + x²) - (15x² + 5x) + (9x + 3)
= 3x²(x + $\frac{1}{3}$) - 15x(x + $\frac{1}{3}$ + 9(x + $\frac{1}{3}$)
⇔ (x+$\frac{1}{3}$)(3x² - 15x + 9)
14) x^4 + 2³ + x² + x + 1
= x^4 + x³ + x³ + x² + x + 1
= (x^4 + x³) + (x³ + x²) + (x + 1)
= x³(x + 1) + x²(x + 1) + (x + 1)
= (x+1)(x³+x²+1)
15) x^4 + 2008x² + 2007x + 2008
= x^4 + 2008x² + 2008x - x + 2008
= (x^4 - x) + (2008x² + 200x + 2008)
= x(x-1)(x² + x + 1) + 2008(x² + x + 1)
= (x² + x + 1)(x² - x + 2008)
16) x^4 + 2010x² + 2009x + 2010
= x^4 + 2010x² + 2010x - x + 2010
= (x^4 - x) + (2010x² + 2010x + 2010)
= x(x-1)(x² + x + 1) + 2010(x² + x + 1)
= (x² + x + 1)(x² - x + 2010)
17) 6x^5 + 15x^4 + 20x³ + 15x² + 6x + 1
= 6x^5 + 3x^4 + 12x^4 + 6x³ + 14x³ + 7x² + 8x² + 4x + 2x + 1
= (6x^5 + 3x^4) + (12x^4 + 6x³) + (14x³ + 7x²) + (8x² + 4x) + (2x + 1)
= 6x^4(x + 0,5) + 12x³(x+0,5) + 14x²(x+0,5) + 8x(x+0,5) + 2(x+0,5)
= (x+0,5)(6x^4 + 12x³ + 14x² + 8x + 2)
