Ontbinden in factoren (2)

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

1. \(-18a^{5}-12a^{4}-2a^{3}\)
2. \(294s^{13}+84s^{8}+6s^{3}\)
3. \(2y^{5}-18y^{3}\)
4. \(-18a^{4}+98a^{2}\)
5. \(-9q^{15}-6q^{10}-q^{5}\)
6. \(20s^{7}-245s^{5}\)
7. \(-8y^{7}-56y^{6}-98y^{5}\)
8. \(32q^{16}-18q^{2}\)
9. \(180y^{10}-300y^{7}+125y^{4}\)
10. \(-54a^{7}+180a^{6}-150a^{5}\)
11. \(-36q^{9}+25q^{3}\)
12. \(50y^{19}-98y^{5}\)

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

Verbetersleutel

1. \(-18a^{5}-12a^{4}-2a^{3}=-2a^{3}(9a^{2}+6a+1)=-2a^{3}(3a+1)^2\)
2. \(294s^{13}+84s^{8}+6s^{3}=6s^{3}(49s^{10}+14s^5+1)=6s^{3}(7s^5+1)^2\)
3. \(2y^{5}-18y^{3}=2y^{3}(y^2-9)=2y^{3}(y-3)(y+3)\)
4. \(-18a^{4}+98a^{2}=-2a^{2}(9a^{2}-49)=-2a^{2}(3a+7)(3a-7)\)
5. \(-9q^{15}-6q^{10}-q^{5}=-q^{5}(9q^{10}+6q^5+1)=-q^{5}(3q^5+1)^2\)
6. \(20s^{7}-245s^{5}=5s^{5}(4s^{2}-49)=5s^{5}(2s+7)(2s-7)\)
7. \(-8y^{7}-56y^{6}-98y^{5}=-2y^{5}(4y^{2}+28y+49)=-2y^{5}(2y+7)^2\)
8. \(32q^{16}-18q^{2}=2q^{2}(16q^{14}-9)=2q^{2}(4q^7+3)(4q^7-3)\)
9. \(180y^{10}-300y^{7}+125y^{4}=5y^{4}(36y^{6}-60y^3+25)=5y^{4}(6y^3-5)^2\)
10. \(-54a^{7}+180a^{6}-150a^{5}=-6a^{5}(9a^{2}-30a+25)=-6a^{5}(3a-5)^2\)
11. \(-36q^{9}+25q^{3}=-q^{3}(36q^{6}-25)=-q^{3}(6q^3+5)(6q^3-5)\)
12. \(50y^{19}-98y^{5}=2y^{5}(25y^{14}-49)=2y^{5}(5y^7+7)(5y^7-7)\)