Ontbinden in factoren (2)

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

1. \(150a^{5}-120a^{4}+24a^{3}\)
2. \(-5b^{5}-90b^{4}-405b^{3}\)
3. \(20p^{6}+20p^{5}+5p^{4}\)
4. \(-5b^{4}+90b^{3}-405b^{2}\)
5. \(180q^{5}-245q^{3}\)
6. \(16q^{10}-24q^{7}+9q^{4}\)
7. \(8q^{6}+40q^{5}+50q^{4}\)
8. \(216b^{7}-6b^{5}\)
9. \(20y^{17}-125y^{5}\)
10. \(5p^{7}-70p^{6}+245p^{5}\)
11. \(-5s^{7}+180s^{5}\)
12. \(9a^{11}-16a^{3}\)

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

Verbetersleutel

1. \(150a^{5}-120a^{4}+24a^{3}=6a^{3}(25a^{2}-20a+4)=6a^{3}(5a-2)^2\)
2. \(-5b^{5}-90b^{4}-405b^{3}=-5b^{3}(b^2+18b+81)=-5b^{3}(b+9)^2\)
3. \(20p^{6}+20p^{5}+5p^{4}=5p^{4}(4p^{2}+4p+1)=5p^{4}(2p+1)^2\)
4. \(-5b^{4}+90b^{3}-405b^{2}=-5b^{2}(b^2-18b+81)=-5b^{2}(b-9)^2\)
5. \(180q^{5}-245q^{3}=5q^{3}(36q^{2}-49)=5q^{3}(6q+7)(6q-7)\)
6. \(16q^{10}-24q^{7}+9q^{4}=q^{4}(16q^{6}-24q^3+9)=q^{4}(4q^3-3)^2\)
7. \(8q^{6}+40q^{5}+50q^{4}=2q^{4}(4q^{2}+20q+25)=2q^{4}(2q+5)^2\)
8. \(216b^{7}-6b^{5}=6b^{5}(36b^{2}-1)=6b^{5}(6b+1)(6b-1)\)
9. \(20y^{17}-125y^{5}=5y^{5}(4y^{12}-25)=5y^{5}(2y^6+5)(2y^6-5)\)
10. \(5p^{7}-70p^{6}+245p^{5}=5p^{5}(p^2-14p+49)=5p^{5}(p-7)^2\)
11. \(-5s^{7}+180s^{5}=-5s^{5}(s^2-36)=-5s^{5}(s-6)(s+6)\)
12. \(9a^{11}-16a^{3}=a^{3}(9a^{8}-16)=a^{3}(3a^4+4)(3a^4-4)\)