Ontbinden in factoren (2)

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

1. \(245s^{11}-140s^{8}+20s^{5}\)
2. \(48a^{9}-75a^{5}\)
3. \(6s^{4}-384s^{2}\)
4. \(-9b^{5}+12b^{4}-4b^{3}\)
5. \(2y^{5}+28y^{4}+98y^{3}\)
6. \(4a^{4}-9a^{2}\)
7. \(-192x^{7}+336x^{5}-147x^{3}\)
8. \(72p^{18}-2p^{4}\)
9. \(108q^{4}+252q^{3}+147q^{2}\)
10. \(-27s^{13}+12s^{3}\)
11. \(-9q^{9}-30q^{6}-25q^{3}\)
12. \(-216q^{14}+150q^{4}\)

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

Verbetersleutel

1. \(245s^{11}-140s^{8}+20s^{5}=5s^{5}(49s^{6}-28s^3+4)=5s^{5}(7s^3-2)^2\)
2. \(48a^{9}-75a^{5}=3a^{5}(16a^{4}-25)=3a^{5}(4a^2+5)(4a^2-5)\)
3. \(6s^{4}-384s^{2}=6s^{2}(s^2-64)=6s^{2}(s-8)(s+8)\)
4. \(-9b^{5}+12b^{4}-4b^{3}=-b^{3}(9b^{2}-12b+4)=-b^{3}(3b-2)^2\)
5. \(2y^{5}+28y^{4}+98y^{3}=2y^{3}(y^2+14y+49)=2y^{3}(y+7)^2\)
6. \(4a^{4}-9a^{2}=a^{2}(4a^{2}-9)=a^{2}(2a+3)(2a-3)\)
7. \(-192x^{7}+336x^{5}-147x^{3}=-3x^{3}(64x^{4}-112x^2+49)=-3x^{3}(8x^2-7)^2\)
8. \(72p^{18}-2p^{4}=2p^{4}(36p^{14}-1)=2p^{4}(6p^7+1)(6p^7-1)\)
9. \(108q^{4}+252q^{3}+147q^{2}=3q^{2}(36q^{2}+84q+49)=3q^{2}(6q+7)^2\)
10. \(-27s^{13}+12s^{3}=-3s^{3}(9s^{10}-4)=-3s^{3}(3s^5+2)(3s^5-2)\)
11. \(-9q^{9}-30q^{6}-25q^{3}=-q^{3}(9q^{6}+30q^3+25)=-q^{3}(3q^3+5)^2\)
12. \(-216q^{14}+150q^{4}=-6q^{4}(36q^{10}-25)=-6q^{4}(6q^5+5)(6q^5-5)\)