Ontbinden in factoren (2)

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

1. \(-3x^{6}+192x^{4}\)
2. \(-125q^{7}-50q^{5}s-5q^{3}s^2\)
3. \(8s^{11}-18s^{5}\)
4. \(16p^{17}-49p^{5}\)
5. \(-25q^{6}-70q^{5}-49q^{4}\)
6. \(216y^{6}-6y^{4}\)
7. \(3a^{5}-147a^{3}\)
8. \(128b^{4}-160b^{3}+50b^{2}\)
9. \(54b^{6}-384b^{4}\)
10. \(-s^{5}+64s^{3}\)
11. \(-3s^{4}+75s^{2}\)
12. \(-6s^{7}+60s^{6}-150s^{5}\)

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

Verbetersleutel

1. \(-3x^{6}+192x^{4}=-3x^{4}(x^2-64)=-3x^{4}(x+8)(x-8)\)
2. \(-125q^{7}-50q^{5}s-5q^{3}s^2=-5q^{3}(25q^{4}+10q^2s+s^2)=-5q^{3}(5q^2+s)^2\)
3. \(8s^{11}-18s^{5}=2s^{5}(4s^{6}-9)=2s^{5}(2s^3+3)(2s^3-3)\)
4. \(16p^{17}-49p^{5}=p^{5}(16p^{12}-49)=p^{5}(4p^6+7)(4p^6-7)\)
5. \(-25q^{6}-70q^{5}-49q^{4}=-q^{4}(25q^{2}+70q+49)=-q^{4}(5q+7)^2\)
6. \(216y^{6}-6y^{4}=6y^{4}(36y^{2}-1)=6y^{4}(6y+1)(6y-1)\)
7. \(3a^{5}-147a^{3}=3a^{3}(a^2-49)=3a^{3}(a+7)(a-7)\)
8. \(128b^{4}-160b^{3}+50b^{2}=2b^{2}(64b^{2}-80b+25)=2b^{2}(8b-5)^2\)
9. \(54b^{6}-384b^{4}=6b^{4}(9b^{2}-64)=6b^{4}(3b+8)(3b-8)\)
10. \(-s^{5}+64s^{3}=-s^{3}(s^2-64)=-s^{3}(s-8)(s+8)\)
11. \(-3s^{4}+75s^{2}=-3s^{2}(s^2-25)=-3s^{2}(s-5)(s+5)\)
12. \(-6s^{7}+60s^{6}-150s^{5}=-6s^{5}(s^2-10s+25)=-6s^{5}(s-5)^2\)