Ontbinden in factoren (2)

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

1. \(2y^{5}-24y^{4}+72y^{3}\)
2. \(-180x^{13}+125x^{3}\)
3. \(48s^{15}-3s^{5}\)
4. \(50q^{13}-8q^{3}\)
5. \(18q^{6}-96q^{5}+128q^{4}\)
6. \(q^{5}-4q^{4}+4q^{3}\)
7. \(-36x^{13}+60x^{9}-25x^{5}\)
8. \(-27s^{8}-90s^{6}-75s^{4}\)
9. \(-75a^{5}+147a^{3}\)
10. \(-72a^{4}+98a^{2}\)
11. \(6q^{7}-384q^{5}\)
12. \(-150p^{7}+240p^{5}q-96p^{3}q^2\)

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

Verbetersleutel

1. \(2y^{5}-24y^{4}+72y^{3}=2y^{3}(y^2-12y+36)=2y^{3}(y-6)^2\)
2. \(-180x^{13}+125x^{3}=-5x^{3}(36x^{10}-25)=-5x^{3}(6x^5+5)(6x^5-5)\)
3. \(48s^{15}-3s^{5}=3s^{5}(16s^{10}-1)=3s^{5}(4s^5+1)(4s^5-1)\)
4. \(50q^{13}-8q^{3}=2q^{3}(25q^{10}-4)=2q^{3}(5q^5+2)(5q^5-2)\)
5. \(18q^{6}-96q^{5}+128q^{4}=2q^{4}(9q^{2}-48q+64)=2q^{4}(3q-8)^2\)
6. \(q^{5}-4q^{4}+4q^{3}=q^{3}(q^2-4q+4)=q^{3}(q-2)^2\)
7. \(-36x^{13}+60x^{9}-25x^{5}=-x^{5}(36x^{8}-60x^4+25)=-x^{5}(6x^4-5)^2\)
8. \(-27s^{8}-90s^{6}-75s^{4}=-3s^{4}(9s^{4}+30s^2+25)=-3s^{4}(3s^2+5)^2\)
9. \(-75a^{5}+147a^{3}=-3a^{3}(25a^{2}-49)=-3a^{3}(5a+7)(5a-7)\)
10. \(-72a^{4}+98a^{2}=-2a^{2}(36a^{2}-49)=-2a^{2}(6a+7)(6a-7)\)
11. \(6q^{7}-384q^{5}=6q^{5}(q^2-64)=6q^{5}(q+8)(q-8)\)
12. \(-150p^{7}+240p^{5}q-96p^{3}q^2=-6p^{3}(25p^{4}-40p^2q+16q^2)=-6p^{3}(5p^2-4q)^2\)