Ontbinden in factoren (2)

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

1. \(6s^{5}+24s^{4}+24s^{3}\)
2. \(-245s^{7}-350s^{5}-125s^{3}\)
3. \(48s^{6}-27s^{4}\)
4. \(-48q^{4}+27q^{2}\)
5. \(-3s^{7}+147s^{5}\)
6. \(36a^{4}-25a^{2}\)
7. \(-96p^{18}+294p^{4}\)
8. \(s^{7}-4s^{6}+4s^{5}\)
9. \(5p^{6}-45p^{4}\)
10. \(32q^{11}+16q^{8}+2q^{5}\)
11. \(-6x^{4}-36x^{3}-54x^{2}\)
12. \(-24b^{13}-24b^{9}s-6b^{5}s^2\)

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

Verbetersleutel

1. \(6s^{5}+24s^{4}+24s^{3}=6s^{3}(s^2+4s+4)=6s^{3}(s+2)^2\)
2. \(-245s^{7}-350s^{5}-125s^{3}=-5s^{3}(49s^{4}+70s^2+25)=-5s^{3}(7s^2+5)^2\)
3. \(48s^{6}-27s^{4}=3s^{4}(16s^{2}-9)=3s^{4}(4s+3)(4s-3)\)
4. \(-48q^{4}+27q^{2}=-3q^{2}(16q^{2}-9)=-3q^{2}(4q+3)(4q-3)\)
5. \(-3s^{7}+147s^{5}=-3s^{5}(s^2-49)=-3s^{5}(s-7)(s+7)\)
6. \(36a^{4}-25a^{2}=a^{2}(36a^{2}-25)=a^{2}(6a+5)(6a-5)\)
7. \(-96p^{18}+294p^{4}=-6p^{4}(16p^{14}-49)=-6p^{4}(4p^7+7)(4p^7-7)\)
8. \(s^{7}-4s^{6}+4s^{5}=s^{5}(s^2-4s+4)=s^{5}(s-2)^2\)
9. \(5p^{6}-45p^{4}=5p^{4}(p^2-9)=5p^{4}(p+3)(p-3)\)
10. \(32q^{11}+16q^{8}+2q^{5}=2q^{5}(16q^{6}+8q^3+1)=2q^{5}(4q^3+1)^2\)
11. \(-6x^{4}-36x^{3}-54x^{2}=-6x^{2}(x^2+6x+9)=-6x^{2}(x+3)^2\)
12. \(-24b^{13}-24b^{9}s-6b^{5}s^2=-6b^{5}(4b^{8}+4b^4s+s^2)=-6b^{5}(2b^4+s)^2\)