Ontbinden in factoren (2)

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

1. \(18q^{5}-24q^{4}+8q^{3}\)
2. \(4a^{15}-9a^{5}\)
3. \(-36q^{4}+25q^{2}\)
4. \(-150a^{16}+216a^{4}\)
5. \(-125y^{5}+5y^{3}\)
6. \(-6s^{5}+150s^{3}\)
7. \(45y^{11}-150y^{7}+125y^{3}\)
8. \(-s^{7}+36s^{5}\)
9. \(-9s^{4}+16s^{2}\)
10. \(20b^{10}+20b^{7}q+5b^{4}q^2\)
11. \(s^{7}+2s^{6}+s^{5}\)
12. \(-5s^{4}+70s^{3}-245s^{2}\)

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

Verbetersleutel

1. \(18q^{5}-24q^{4}+8q^{3}=2q^{3}(9q^{2}-12q+4)=2q^{3}(3q-2)^2\)
2. \(4a^{15}-9a^{5}=a^{5}(4a^{10}-9)=a^{5}(2a^5+3)(2a^5-3)\)
3. \(-36q^{4}+25q^{2}=-q^{2}(36q^{2}-25)=-q^{2}(6q+5)(6q-5)\)
4. \(-150a^{16}+216a^{4}=-6a^{4}(25a^{12}-36)=-6a^{4}(5a^6+6)(5a^6-6)\)
5. \(-125y^{5}+5y^{3}=-5y^{3}(25y^{2}-1)=-5y^{3}(5y+1)(5y-1)\)
6. \(-6s^{5}+150s^{3}=-6s^{3}(s^2-25)=-6s^{3}(s-5)(s+5)\)
7. \(45y^{11}-150y^{7}+125y^{3}=5y^{3}(9y^{8}-30y^4+25)=5y^{3}(3y^4-5)^2\)
8. \(-s^{7}+36s^{5}=-s^{5}(s^2-36)=-s^{5}(s-6)(s+6)\)
9. \(-9s^{4}+16s^{2}=-s^{2}(9s^{2}-16)=-s^{2}(3s+4)(3s-4)\)
10. \(20b^{10}+20b^{7}q+5b^{4}q^2=5b^{4}(4b^{6}+4b^3q+q^2)=5b^{4}(2b^3+q)^2\)
11. \(s^{7}+2s^{6}+s^{5}=s^{5}(s^2+2s+1)=s^{5}(s+1)^2\)
12. \(-5s^{4}+70s^{3}-245s^{2}=-5s^{2}(s^2-14s+49)=-5s^{2}(s-7)^2\)