Ontbinden in factoren (2)

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

1. \(-24p^{11}-24p^{8}-6p^{5}\)
2. \(-16s^{12}+24s^{8}-9s^{4}\)
3. \(75a^{9}-3a^{3}\)
4. \(16q^{7}-49q^{5}\)
5. \(6p^{7}-384p^{5}\)
6. \(6x^{5}-384x^{3}\)
7. \(80a^{11}+40a^{8}+5a^{5}\)
8. \(-54y^{10}-144y^{6}-96y^{2}\)
9. \(-384q^{15}+672q^{10}-294q^{5}\)
10. \(384y^{9}+288y^{7}+54y^{5}\)
11. \(-16s^{9}-24s^{7}-9s^{5}\)
12. \(-6q^{5}+216q^{3}\)

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

Verbetersleutel

1. \(-24p^{11}-24p^{8}-6p^{5}=-6p^{5}(4p^{6}+4p^3+1)=-6p^{5}(2p^3+1)^2\)
2. \(-16s^{12}+24s^{8}-9s^{4}=-s^{4}(16s^{8}-24s^4+9)=-s^{4}(4s^4-3)^2\)
3. \(75a^{9}-3a^{3}=3a^{3}(25a^{6}-1)=3a^{3}(5a^3+1)(5a^3-1)\)
4. \(16q^{7}-49q^{5}=q^{5}(16q^{2}-49)=q^{5}(4q+7)(4q-7)\)
5. \(6p^{7}-384p^{5}=6p^{5}(p^2-64)=6p^{5}(p+8)(p-8)\)
6. \(6x^{5}-384x^{3}=6x^{3}(x^2-64)=6x^{3}(x-8)(x+8)\)
7. \(80a^{11}+40a^{8}+5a^{5}=5a^{5}(16a^{6}+8a^3+1)=5a^{5}(4a^3+1)^2\)
8. \(-54y^{10}-144y^{6}-96y^{2}=-6y^{2}(9y^{8}+24y^4+16)=-6y^{2}(3y^4+4)^2\)
9. \(-384q^{15}+672q^{10}-294q^{5}=-6q^{5}(64q^{10}-112q^5+49)=-6q^{5}(8q^5-7)^2\)
10. \(384y^{9}+288y^{7}+54y^{5}=6y^{5}(64y^{4}+48y^2+9)=6y^{5}(8y^2+3)^2\)
11. \(-16s^{9}-24s^{7}-9s^{5}=-s^{5}(16s^{4}+24s^2+9)=-s^{5}(4s^2+3)^2\)
12. \(-6q^{5}+216q^{3}=-6q^{3}(q^2-36)=-6q^{3}(q-6)(q+6)\)