Ontbinden in factoren (2)

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

1. \(-80x^{7}+120x^{6}-45x^{5}\)
2. \(-5b^{7}+125b^{5}\)
3. \(s^{6}-6s^{5}+9s^{4}\)
4. \(2a^{6}-72a^{4}\)
5. \(-72p^{5}-168p^{4}-98p^{3}\)
6. \(180b^{11}-5b^{5}\)
7. \(-8y^{5}+2y^{3}\)
8. \(125p^{13}-5p^{5}\)
9. \(108a^{18}-75a^{4}\)
10. \(216p^{10}+360p^{6}s+150p^{2}s^2\)
11. \(-s^{5}+6s^{4}-9s^{3}\)
12. \(96a^{13}-144a^{9}p+54a^{5}p^2\)

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

Verbetersleutel

1. \(-80x^{7}+120x^{6}-45x^{5}=-5x^{5}(16x^{2}-24x+9)=-5x^{5}(4x-3)^2\)
2. \(-5b^{7}+125b^{5}=-5b^{5}(b^2-25)=-5b^{5}(b-5)(b+5)\)
3. \(s^{6}-6s^{5}+9s^{4}=s^{4}(s^2-6s+9)=s^{4}(s-3)^2\)
4. \(2a^{6}-72a^{4}=2a^{4}(a^2-36)=2a^{4}(a-6)(a+6)\)
5. \(-72p^{5}-168p^{4}-98p^{3}=-2p^{3}(36p^{2}+84p+49)=-2p^{3}(6p+7)^2\)
6. \(180b^{11}-5b^{5}=5b^{5}(36b^{6}-1)=5b^{5}(6b^3+1)(6b^3-1)\)
7. \(-8y^{5}+2y^{3}=-2y^{3}(4y^{2}-1)=-2y^{3}(2y+1)(2y-1)\)
8. \(125p^{13}-5p^{5}=5p^{5}(25p^{8}-1)=5p^{5}(5p^4+1)(5p^4-1)\)
9. \(108a^{18}-75a^{4}=3a^{4}(36a^{14}-25)=3a^{4}(6a^7+5)(6a^7-5)\)
10. \(216p^{10}+360p^{6}s+150p^{2}s^2=6p^{2}(36p^{8}+60p^4s+25s^2)=6p^{2}(6p^4+5s)^2\)
11. \(-s^{5}+6s^{4}-9s^{3}=-s^{3}(s^2-6s+9)=-s^{3}(s-3)^2\)
12. \(96a^{13}-144a^{9}p+54a^{5}p^2=6a^{5}(16a^{8}-24a^4p+9p^2)=6a^{5}(4a^4-3p)^2\)