Ontbinden in factoren (2)

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

1. \(-5a^{7}-90a^{6}-405a^{5}\)
2. \(2p^{6}-24p^{5}+72p^{4}\)
3. \(50q^{5}+120q^{4}+72q^{3}\)
4. \(128b^{7}-224b^{5}+98b^{3}\)
5. \(-q^{7}+64q^{5}\)
6. \(180x^{7}-245x^{3}\)
7. \(54p^{12}-294p^{4}\)
8. \(2q^{5}+16q^{4}+32q^{3}\)
9. \(150q^{7}-240q^{6}+96q^{5}\)
10. \(-54p^{5}+96p^{3}\)
11. \(-6b^{6}-60b^{5}-150b^{4}\)
12. \(75a^{15}-27a^{5}\)

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

Verbetersleutel

1. \(-5a^{7}-90a^{6}-405a^{5}=-5a^{5}(a^2+18a+81)=-5a^{5}(a+9)^2\)
2. \(2p^{6}-24p^{5}+72p^{4}=2p^{4}(p^2-12p+36)=2p^{4}(p-6)^2\)
3. \(50q^{5}+120q^{4}+72q^{3}=2q^{3}(25q^{2}+60q+36)=2q^{3}(5q+6)^2\)
4. \(128b^{7}-224b^{5}+98b^{3}=2b^{3}(64b^{4}-112b^2+49)=2b^{3}(8b^2-7)^2\)
5. \(-q^{7}+64q^{5}=-q^{5}(q^2-64)=-q^{5}(q-8)(q+8)\)
6. \(180x^{7}-245x^{3}=5x^{3}(36x^{4}-49)=5x^{3}(6x^2+7)(6x^2-7)\)
7. \(54p^{12}-294p^{4}=6p^{4}(9p^{8}-49)=6p^{4}(3p^4+7)(3p^4-7)\)
8. \(2q^{5}+16q^{4}+32q^{3}=2q^{3}(q^2+8q+16)=2q^{3}(q+4)^2\)
9. \(150q^{7}-240q^{6}+96q^{5}=6q^{5}(25q^{2}-40q+16)=6q^{5}(5q-4)^2\)
10. \(-54p^{5}+96p^{3}=-6p^{3}(9p^{2}-16)=-6p^{3}(3p+4)(3p-4)\)
11. \(-6b^{6}-60b^{5}-150b^{4}=-6b^{4}(b^2+10b+25)=-6b^{4}(b+5)^2\)
12. \(75a^{15}-27a^{5}=3a^{5}(25a^{10}-9)=3a^{5}(5a^5+3)(5a^5-3)\)