Leysa {l}{y(y+3)-21}{y^2+3y+21}{y^2+3y-21}{y^2+21}{y(y+3)(y+7)}{(y-3)(y-7)}

$$\left. \begin{array} { l } { y ( y + 3 ) - 21 } \\ { y ^ { 2 } + 3 y + 21 } \\ { y ^ { 2 } + 3 y - 21 } \\ { y ^ { 2 } + 21 } \\ { y ( y + 3 ) ( y + 7 ) } \\ { ( y - 3 ) ( y - 7 ) } \end{array} \right.$$

Sjaldgæfasta margfeldi

$$y\left(y^{10}+6y^{9}-28y^{8}-222y^{7}-1551y^{6}-4662y^{5}+18585y^{4}+55566y^{3}+426006y^{2}-4084101\right)$$

Lausnarskref

Þættaðu segðir sem hafa ekki þegar verið þættaðar.

$$y\left(y+3\right)-21=\left(y-\left(-\frac{1}{2}\sqrt{93}-\frac{3}{2}\right)\right)\left(y-\left(\frac{1}{2}\sqrt{93}-\frac{3}{2}\right)\right) y^{2}+3y-21=\left(y-\left(-\frac{1}{2}\sqrt{93}-\frac{3}{2}\right)\right)\left(y-\left(\frac{1}{2}\sqrt{93}-\frac{3}{2}\right)\right)$$

Greindu alla þætti og hæsta veldi þeirra í öllum segðum. Margfaldaðu hæstu veldi þessara þátta til að finna minnsta samfeldi.

$$y\left(y^{10}+6y^{9}-28y^{8}-222y^{7}-1551y^{6}-4662y^{5}+18585y^{4}+55566y^{3}+426006y^{2}-4084101\right)$$

Víkkaðu segðina út.

$$y^{11}+6y^{10}-28y^{9}-222y^{8}-1551y^{7}-4662y^{6}+18585y^{5}+55566y^{4}+426006y^{3}-4084101y$$

Meta

$$y\left(y+3\right)-21,\ y^{2}+3y+21,\ y^{2}+3y-21,\ y^{2}+21,\ y\left(y+3\right)\left(y+7\right),\ \left(y-7\right)\left(y-3\right)$$