Ontbinden in factoren (2)

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

1. \(-147a^{10}-210a^{6}-75a^{2}\)
2. \(-4s^{5}-4s^{4}-s^{3}\)
3. \(6p^{7}-54p^{5}\)
4. \(320p^{7}+80p^{6}+5p^{5}\)
5. \(-150a^{4}+6a^{2}\)
6. \(5s^{4}+50s^{3}+125s^{2}\)
7. \(-72a^{13}-24a^{8}-2a^{3}\)
8. \(64q^{9}+48q^{6}+9q^{3}\)
9. \(24a^{13}-54a^{5}\)
10. \(-36b^{14}-12b^{9}-b^{4}\)
11. \(-6s^{4}+54s^{2}\)
12. \(147x^{6}-378x^{5}+243x^{4}\)

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

Verbetersleutel

1. \(-147a^{10}-210a^{6}-75a^{2}=-3a^{2}(49a^{8}+70a^4+25)=-3a^{2}(7a^4+5)^2\)
2. \(-4s^{5}-4s^{4}-s^{3}=-s^{3}(4s^{2}+4s+1)=-s^{3}(2s+1)^2\)
3. \(6p^{7}-54p^{5}=6p^{5}(p^2-9)=6p^{5}(p+3)(p-3)\)
4. \(320p^{7}+80p^{6}+5p^{5}=5p^{5}(64p^{2}+16p+1)=5p^{5}(8p+1)^2\)
5. \(-150a^{4}+6a^{2}=-6a^{2}(25a^{2}-1)=-6a^{2}(5a+1)(5a-1)\)
6. \(5s^{4}+50s^{3}+125s^{2}=5s^{2}(s^2+10s+25)=5s^{2}(s+5)^2\)
7. \(-72a^{13}-24a^{8}-2a^{3}=-2a^{3}(36a^{10}+12a^5+1)=-2a^{3}(6a^5+1)^2\)
8. \(64q^{9}+48q^{6}+9q^{3}=q^{3}(64q^{6}+48q^3+9)=q^{3}(8q^3+3)^2\)
9. \(24a^{13}-54a^{5}=6a^{5}(4a^{8}-9)=6a^{5}(2a^4+3)(2a^4-3)\)
10. \(-36b^{14}-12b^{9}-b^{4}=-b^{4}(36b^{10}+12b^5+1)=-b^{4}(6b^5+1)^2\)
11. \(-6s^{4}+54s^{2}=-6s^{2}(s^2-9)=-6s^{2}(s-3)(s+3)\)
12. \(147x^{6}-378x^{5}+243x^{4}=3x^{4}(49x^{2}-126x+81)=3x^{4}(7x-9)^2\)