Ontbinden in factoren (2)

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

1. \(-192b^{6}-240b^{5}-75b^{4}\)
2. \(-36s^{6}+60s^{5}-25s^{4}\)
3. \(-9a^{6}+30a^{4}q-25a^{2}q^2\)
4. \(-36b^{17}+25b^{3}\)
5. \(320b^{10}+240b^{7}y+45b^{4}y^2\)
6. \(-4p^{9}-4p^{7}-p^{5}\)
7. \(6x^{7}-96x^{5}\)
8. \(3p^{6}+42p^{5}+147p^{4}\)
9. \(3a^{4}-24a^{3}+48a^{2}\)
10. \(-32p^{4}+2p^{2}\)
11. \(180q^{14}-245q^{2}\)
12. \(-20s^{7}+5s^{5}\)

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

Verbetersleutel

1. \(-192b^{6}-240b^{5}-75b^{4}=-3b^{4}(64b^{2}+80b+25)=-3b^{4}(8b+5)^2\)
2. \(-36s^{6}+60s^{5}-25s^{4}=-s^{4}(36s^{2}-60s+25)=-s^{4}(6s-5)^2\)
3. \(-9a^{6}+30a^{4}q-25a^{2}q^2=-a^{2}(9a^{4}-30a^2q+25q^2)=-a^{2}(3a^2-5q)^2\)
4. \(-36b^{17}+25b^{3}=-b^{3}(36b^{14}-25)=-b^{3}(6b^7+5)(6b^7-5)\)
5. \(320b^{10}+240b^{7}y+45b^{4}y^2=5b^{4}(64b^{6}+48b^3y+9y^2)=5b^{4}(8b^3+3y)^2\)
6. \(-4p^{9}-4p^{7}-p^{5}=-p^{5}(4p^{4}+4p^2+1)=-p^{5}(2p^2+1)^2\)
7. \(6x^{7}-96x^{5}=6x^{5}(x^2-16)=6x^{5}(x-4)(x+4)\)
8. \(3p^{6}+42p^{5}+147p^{4}=3p^{4}(p^2+14p+49)=3p^{4}(p+7)^2\)
9. \(3a^{4}-24a^{3}+48a^{2}=3a^{2}(a^2-8a+16)=3a^{2}(a-4)^2\)
10. \(-32p^{4}+2p^{2}=-2p^{2}(16p^{2}-1)=-2p^{2}(4p+1)(4p-1)\)
11. \(180q^{14}-245q^{2}=5q^{2}(36q^{12}-49)=5q^{2}(6q^6+7)(6q^6-7)\)
12. \(-20s^{7}+5s^{5}=-5s^{5}(4s^{2}-1)=-5s^{5}(2s+1)(2s-1)\)