Ontbinden in factoren (2)

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

1. \(3s^{5}-12s^{4}+12s^{3}\)
2. \(9a^{9}+24a^{6}+16a^{3}\)
3. \(-45p^{9}-30p^{7}-5p^{5}\)
4. \(-294q^{4}+168q^{3}-24q^{2}\)
5. \(-36a^{7}+60a^{5}-25a^{3}\)
6. \(2s^{5}+12s^{4}+18s^{3}\)
7. \(-6p^{5}+12p^{4}-6p^{3}\)
8. \(-216x^{9}+6x^{5}\)
9. \(20y^{4}-5y^{2}\)
10. \(-36b^{10}+49b^{2}\)
11. \(50s^{4}-40s^{3}+8s^{2}\)
12. \(-8y^{5}-8y^{4}-2y^{3}\)

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

Verbetersleutel

1. \(3s^{5}-12s^{4}+12s^{3}=3s^{3}(s^2-4s+4)=3s^{3}(s-2)^2\)
2. \(9a^{9}+24a^{6}+16a^{3}=a^{3}(9a^{6}+24a^3+16)=a^{3}(3a^3+4)^2\)
3. \(-45p^{9}-30p^{7}-5p^{5}=-5p^{5}(9p^{4}+6p^2+1)=-5p^{5}(3p^2+1)^2\)
4. \(-294q^{4}+168q^{3}-24q^{2}=-6q^{2}(49q^{2}-28q+4)=-6q^{2}(7q-2)^2\)
5. \(-36a^{7}+60a^{5}-25a^{3}=-a^{3}(36a^{4}-60a^2+25)=-a^{3}(6a^2-5)^2\)
6. \(2s^{5}+12s^{4}+18s^{3}=2s^{3}(s^2+6s+9)=2s^{3}(s+3)^2\)
7. \(-6p^{5}+12p^{4}-6p^{3}=-6p^{3}(p^2-2p+1)=-6p^{3}(p-1)^2\)
8. \(-216x^{9}+6x^{5}=-6x^{5}(36x^{4}-1)=-6x^{5}(6x^2+1)(6x^2-1)\)
9. \(20y^{4}-5y^{2}=5y^{2}(4y^{2}-1)=5y^{2}(2y+1)(2y-1)\)
10. \(-36b^{10}+49b^{2}=-b^{2}(36b^{8}-49)=-b^{2}(6b^4+7)(6b^4-7)\)
11. \(50s^{4}-40s^{3}+8s^{2}=2s^{2}(25s^{2}-20s+4)=2s^{2}(5s-2)^2\)
12. \(-8y^{5}-8y^{4}-2y^{3}=-2y^{3}(4y^{2}+4y+1)=-2y^{3}(2y+1)^2\)