Solve x^99-5*096+x^2

$$x ^ { 99 } - 5 \cdot 096 + x ^ { 2 }$$

Evaluate

$$x^{99}+x^{2}$$

Solution Steps

Multiply 5 and 0 to get 0.

$$x^{99}-0\times 96+x^{2}$$

Multiply 0 and 96 to get 0.

$$x^{99}-0+x^{2}$$

Multiply -1 and 0 to get 0.

$$x^{99}+0+x^{2}$$

Anything plus zero gives itself.

$$x^{99}+x^{2}$$

Factor

$$\left(x+1\right)x^{2}\left(x^{96}-x^{95}+x^{94}-x^{93}+x^{92}-x^{91}+x^{90}-x^{89}+x^{88}-x^{87}+x^{86}-x^{85}+x^{84}-x^{83}+x^{82}-x^{81}+x^{80}-x^{79}+x^{78}-x^{77}+x^{76}-x^{75}+x^{74}-x^{73}+x^{72}-x^{71}+x^{70}-x^{69}+x^{68}-x^{67}+x^{66}-x^{65}+x^{64}-x^{63}+x^{62}-x^{61}+x^{60}-x^{59}+x^{58}-x^{57}+x^{56}-x^{55}+x^{54}-x^{53}+x^{52}-x^{51}+x^{50}-x^{49}+x^{48}-x^{47}+x^{46}-x^{45}+x^{44}-x^{43}+x^{42}-x^{41}+x^{40}-x^{39}+x^{38}-x^{37}+x^{36}-x^{35}+x^{34}-x^{33}+x^{32}-x^{31}+x^{30}-x^{29}+x^{28}-x^{27}+x^{26}-x^{25}+x^{24}-x^{23}+x^{22}-x^{21}+x^{20}-x^{19}+x^{18}-x^{17}+x^{16}-x^{15}+x^{14}-x^{13}+x^{12}-x^{11}+x^{10}-x^{9}+x^{8}-x^{7}+x^{6}-x^{5}+x^{4}-x^{3}+x^{2}-x+1\right)$$

Solution Steps

Multiply and combine like terms.

$$x^{99}+x^{2}$$

Factor out x^{2}.

$$x^{2}\left(x^{97}+1\right)$$

Consider x^{97}+1. By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 1 and q divides the leading coefficient 1. One such root is -1. Factor the polynomial by dividing it by x+1.

$$\left(x+1\right)\left(x^{96}-x^{95}+x^{94}-x^{93}+x^{92}-x^{91}+x^{90}-x^{89}+x^{88}-x^{87}+x^{86}-x^{85}+x^{84}-x^{83}+x^{82}-x^{81}+x^{80}-x^{79}+x^{78}-x^{77}+x^{76}-x^{75}+x^{74}-x^{73}+x^{72}-x^{71}+x^{70}-x^{69}+x^{68}-x^{67}+x^{66}-x^{65}+x^{64}-x^{63}+x^{62}-x^{61}+x^{60}-x^{59}+x^{58}-x^{57}+x^{56}-x^{55}+x^{54}-x^{53}+x^{52}-x^{51}+x^{50}-x^{49}+x^{48}-x^{47}+x^{46}-x^{45}+x^{44}-x^{43}+x^{42}-x^{41}+x^{40}-x^{39}+x^{38}-x^{37}+x^{36}-x^{35}+x^{34}-x^{33}+x^{32}-x^{31}+x^{30}-x^{29}+x^{28}-x^{27}+x^{26}-x^{25}+x^{24}-x^{23}+x^{22}-x^{21}+x^{20}-x^{19}+x^{18}-x^{17}+x^{16}-x^{15}+x^{14}-x^{13}+x^{12}-x^{11}+x^{10}-x^{9}+x^{8}-x^{7}+x^{6}-x^{5}+x^{4}-x^{3}+x^{2}-x+1\right)$$

Rewrite the complete factored expression. Polynomial x^{96}-x^{95}+x^{94}-x^{93}+x^{92}-x^{91}+x^{90}-x^{89}+x^{88}-x^{87}+x^{86}-x^{85}+x^{84}-x^{83}+x^{82}-x^{81}+x^{80}-x^{79}+x^{78}-x^{77}+x^{76}-x^{75}+x^{74}-x^{73}+x^{72}-x^{71}+x^{70}-x^{69}+x^{68}-x^{67}+x^{66}-x^{65}+x^{64}-x^{63}+x^{62}-x^{61}+x^{60}-x^{59}+x^{58}-x^{57}+x^{56}-x^{55}+x^{54}-x^{53}+x^{52}-x^{51}+x^{50}-x^{49}+x^{48}-x^{47}+x^{46}-x^{45}+x^{44}-x^{43}+x^{42}-x^{41}+x^{40}-x^{39}+x^{38}-x^{37}+x^{36}-x^{35}+x^{34}-x^{33}+x^{32}-x^{31}+x^{30}-x^{29}+x^{28}-x^{27}+x^{26}-x^{25}+x^{24}-x^{23}+x^{22}-x^{21}+x^{20}-x^{19}+x^{18}-x^{17}+x^{16}-x^{15}+x^{14}-x^{13}+x^{12}-x^{11}+x^{10}-x^{9}+x^{8}-x^{7}+x^{6}-x^{5}+x^{4}-x^{3}+x^{2}-x+1 is not factored since it does not have any rational roots.

$$x^{2}\left(x+1\right)\left(x^{96}-x^{95}+x^{94}-x^{93}+x^{92}-x^{91}+x^{90}-x^{89}+x^{88}-x^{87}+x^{86}-x^{85}+x^{84}-x^{83}+x^{82}-x^{81}+x^{80}-x^{79}+x^{78}-x^{77}+x^{76}-x^{75}+x^{74}-x^{73}+x^{72}-x^{71}+x^{70}-x^{69}+x^{68}-x^{67}+x^{66}-x^{65}+x^{64}-x^{63}+x^{62}-x^{61}+x^{60}-x^{59}+x^{58}-x^{57}+x^{56}-x^{55}+x^{54}-x^{53}+x^{52}-x^{51}+x^{50}-x^{49}+x^{48}-x^{47}+x^{46}-x^{45}+x^{44}-x^{43}+x^{42}-x^{41}+x^{40}-x^{39}+x^{38}-x^{37}+x^{36}-x^{35}+x^{34}-x^{33}+x^{32}-x^{31}+x^{30}-x^{29}+x^{28}-x^{27}+x^{26}-x^{25}+x^{24}-x^{23}+x^{22}-x^{21}+x^{20}-x^{19}+x^{18}-x^{17}+x^{16}-x^{15}+x^{14}-x^{13}+x^{12}-x^{11}+x^{10}-x^{9}+x^{8}-x^{7}+x^{6}-x^{5}+x^{4}-x^{3}+x^{2}-x+1\right)$$