Issolvi x^6+2x^5-2x^3-x^2

$$x ^ { 6 } + 2 x ^ { 5 } - 2 x ^ { 3 } - x ^ { 2 }$$

Fattur

$$\left(x-1\right)x^{2}\left(x+1\right)^{3}$$

Passi tas-Soluzzjonijiet

Iffattura 'l barra x^{2}.

$$x^{2}\left(x^{4}+2x^{3}-2x-1\right)$$

Ikkunsidra li x^{4}+2x^{3}-2x-1. Sib fattur wieħed fil-forma x^{k}+m, fejn x^{k} jaqsam il-monomial bl-ogħla poter x^{4} u m jaqsam il-fattur tal-kostanti -1. Fattur wieħed bħal dan huwa x^{2}-1. Iffattura l-polynomial billi tiddividih b'dan il-fattur.

$$\left(x^{2}-1\right)\left(x^{2}+2x+1\right)$$

Ikkunsidra li x^{2}-1. Erġa' ikteb x^{2}-1 bħala x^{2}-1^{2}. Id-differenza tal-kwadrati tista' tiġi fatturata billi tuża r-regola: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-1\right)\left(x+1\right)$$

Ikkunsidra li x^{2}+2x+1. Uża l-formula tal-kwadru perfett, a^{2}+2ab+b^{2}=\left(a+b\right)^{2}, fejn a=x u b=1.

$$\left(x+1\right)^{2}$$

Erġa' ikteb l-espressjoni ffatturata kompluta.

$$x^{2}\left(x-1\right)\left(x+1\right)^{3}$$

Evalwa

$$\left(x-1\right)x^{2}\left(x+1\right)^{3}$$