Ontbinden in factoren (2)

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Zonder de gemeenschappelijke factor af. Ontbind verder in factoren indien mogelijk.

1. \(-5s^{7}+5s^{5}\)
2. \(245a^{7}-140a^{6}+20a^{5}\)
3. \(-4q^{8}-4q^{5}-q^{2}\)
4. \(-128q^{13}-32q^{8}-2q^{3}\)
5. \(72y^{10}-120y^{7}+50y^{4}\)
6. \(5q^{4}-60q^{3}+180q^{2}\)
7. \(24s^{6}-150s^{2}\)
8. \(3q^{6}-24q^{5}+48q^{4}\)
9. \(-p^{4}-2p^{3}-p^{2}\)
10. \(18b^{17}-98b^{3}\)
11. \(-45b^{14}-30b^{9}-5b^{4}\)
12. \(-9s^{17}+s^{5}\)

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Zonder de gemeenschappelijke factor af. Ontbind verder in factoren indien mogelijk.

Verbetersleutel

1. \(-5s^{7}+5s^{5}=-5s^{5}(s^2-1)=-5s^{5}(s+1)(s-1)\)
2. \(245a^{7}-140a^{6}+20a^{5}=5a^{5}(49a^{2}-28a+4)=5a^{5}(7a-2)^2\)
3. \(-4q^{8}-4q^{5}-q^{2}=-q^{2}(4q^{6}+4q^3+1)=-q^{2}(2q^3+1)^2\)
4. \(-128q^{13}-32q^{8}-2q^{3}=-2q^{3}(64q^{10}+16q^5+1)=-2q^{3}(8q^5+1)^2\)
5. \(72y^{10}-120y^{7}+50y^{4}=2y^{4}(36y^{6}-60y^3+25)=2y^{4}(6y^3-5)^2\)
6. \(5q^{4}-60q^{3}+180q^{2}=5q^{2}(q^2-12q+36)=5q^{2}(q-6)^2\)
7. \(24s^{6}-150s^{2}=6s^{2}(4s^{4}-25)=6s^{2}(2s^2+5)(2s^2-5)\)
8. \(3q^{6}-24q^{5}+48q^{4}=3q^{4}(q^2-8q+16)=3q^{4}(q-4)^2\)
9. \(-p^{4}-2p^{3}-p^{2}=-p^{2}(p^2+2p+1)=-p^{2}(p+1)^2\)
10. \(18b^{17}-98b^{3}=2b^{3}(9b^{14}-49)=2b^{3}(3b^7+7)(3b^7-7)\)
11. \(-45b^{14}-30b^{9}-5b^{4}=-5b^{4}(9b^{10}+6b^5+1)=-5b^{4}(3b^5+1)^2\)
12. \(-9s^{17}+s^{5}=-s^{5}(9s^{12}-1)=-s^{5}(3s^6+1)(3s^6-1)\)