Question

Розклади на множники y3−y2−0,5y+0,125.​

Answer 1

$y^3-y^2-\frac{y}{2}+\frac{1}{8}=(y^3+(\frac{1}{2})^3)-y(y+\frac{1}{2})=$

$=(y+\frac{1}{2})(y^2-y\cdot \frac{1}{2}+(\frac{1}{2})^2)-y(y+\frac{1}{2})=(y+\frac{1}{2})(y^2-\frac{y}{2}+\frac{1}{4}-y)=$

$=(y+0,5)(y^2-\frac{3}{2}y+\frac{1}{4})=(y+0,5)((y-\frac{3}{4})^2-\frac{5}{16})=$

$(y+0,5)(y-\frac{3}{4}-\frac{\sqrt{5}}{4})(y-\frac{3}{4}+\frac{\sqrt{5}}{4})$