Ontbinden in factoren (2)

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

1. \(3q^{5}-18q^{4}+27q^{3}\)
2. \(-36b^{15}+60b^{10}-25b^{5}\)
3. \(8x^{14}-2x^{2}\)
4. \(p^{4}-16p^{2}\)
5. \(8q^{5}-50q^{3}\)
6. \(-2x^{5}+32x^{3}\)
7. \(24s^{6}+24s^{5}+6s^{4}\)
8. \(2p^{7}-2p^{5}\)
9. \(27a^{4}-36a^{3}+12a^{2}\)
10. \(-20p^{15}-20p^{10}q-5p^{5}q^2\)
11. \(-16s^{4}-40s^{3}-25s^{2}\)
12. \(12q^{12}+12q^{8}+3q^{4}\)

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

Verbetersleutel

1. \(3q^{5}-18q^{4}+27q^{3}=3q^{3}(q^2-6q+9)=3q^{3}(q-3)^2\)
2. \(-36b^{15}+60b^{10}-25b^{5}=-b^{5}(36b^{10}-60b^5+25)=-b^{5}(6b^5-5)^2\)
3. \(8x^{14}-2x^{2}=2x^{2}(4x^{12}-1)=2x^{2}(2x^6+1)(2x^6-1)\)
4. \(p^{4}-16p^{2}=p^{2}(p^2-16)=p^{2}(p+4)(p-4)\)
5. \(8q^{5}-50q^{3}=2q^{3}(4q^{2}-25)=2q^{3}(2q+5)(2q-5)\)
6. \(-2x^{5}+32x^{3}=-2x^{3}(x^2-16)=-2x^{3}(x-4)(x+4)\)
7. \(24s^{6}+24s^{5}+6s^{4}=6s^{4}(4s^{2}+4s+1)=6s^{4}(2s+1)^2\)
8. \(2p^{7}-2p^{5}=2p^{5}(p^2-1)=2p^{5}(p-1)(p+1)\)
9. \(27a^{4}-36a^{3}+12a^{2}=3a^{2}(9a^{2}-12a+4)=3a^{2}(3a-2)^2\)
10. \(-20p^{15}-20p^{10}q-5p^{5}q^2=-5p^{5}(4p^{10}+4p^5q+q^2)=-5p^{5}(2p^5+q)^2\)
11. \(-16s^{4}-40s^{3}-25s^{2}=-s^{2}(16s^{2}+40s+25)=-s^{2}(4s+5)^2\)
12. \(12q^{12}+12q^{8}+3q^{4}=3q^{4}(4q^{8}+4q^4+1)=3q^{4}(2q^4+1)^2\)