Ontbinden in factoren (2)

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

1. \(-96s^{21}+150s^{5}\)
2. \(98b^{6}+28b^{5}+2b^{4}\)
3. \(b^{5}+18b^{4}+81b^{3}\)
4. \(24x^{5}-150x^{3}\)
5. \(75a^{7}-3a^{5}\)
6. \(20p^{5}-245p^{3}\)
7. \(-3q^{5}+12q^{3}\)
8. \(-3q^{7}+36q^{6}-108q^{5}\)
9. \(-216x^{6}+150x^{4}\)
10. \(-6a^{5}+216a^{3}\)
11. \(-24p^{6}+294p^{4}\)
12. \(24s^{14}+120s^{9}+150s^{4}\)

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

Verbetersleutel

1. \(-96s^{21}+150s^{5}=-6s^{5}(16s^{16}-25)=-6s^{5}(4s^8+5)(4s^8-5)\)
2. \(98b^{6}+28b^{5}+2b^{4}=2b^{4}(49b^{2}+14b+1)=2b^{4}(7b+1)^2\)
3. \(b^{5}+18b^{4}+81b^{3}=b^{3}(b^2+18b+81)=b^{3}(b+9)^2\)
4. \(24x^{5}-150x^{3}=6x^{3}(4x^{2}-25)=6x^{3}(2x+5)(2x-5)\)
5. \(75a^{7}-3a^{5}=3a^{5}(25a^{2}-1)=3a^{5}(5a+1)(5a-1)\)
6. \(20p^{5}-245p^{3}=5p^{3}(4p^{2}-49)=5p^{3}(2p+7)(2p-7)\)
7. \(-3q^{5}+12q^{3}=-3q^{3}(q^2-4)=-3q^{3}(q+2)(q-2)\)
8. \(-3q^{7}+36q^{6}-108q^{5}=-3q^{5}(q^2-12q+36)=-3q^{5}(q-6)^2\)
9. \(-216x^{6}+150x^{4}=-6x^{4}(36x^{2}-25)=-6x^{4}(6x+5)(6x-5)\)
10. \(-6a^{5}+216a^{3}=-6a^{3}(a^2-36)=-6a^{3}(a+6)(a-6)\)
11. \(-24p^{6}+294p^{4}=-6p^{4}(4p^{2}-49)=-6p^{4}(2p+7)(2p-7)\)
12. \(24s^{14}+120s^{9}+150s^{4}=6s^{4}(4s^{10}+20s^5+25)=6s^{4}(2s^5+5)^2\)