Ontbinden in factoren (2)

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

1. \(-6s^{7}+6s^{5}\)
2. \(-6a^{5}-108a^{4}-486a^{3}\)
3. \(-2p^{6}-8p^{5}-8p^{4}\)
4. \(2x^{7}-32x^{5}\)
5. \(45b^{6}+30b^{5}+5b^{4}\)
6. \(216y^{8}+72y^{5}+6y^{2}\)
7. \(-48a^{4}-24a^{3}-3a^{2}\)
8. \(-54p^{12}-36p^{7}y-6p^{2}y^2\)
9. \(27b^{7}+144b^{6}+192b^{5}\)
10. \(-98q^{6}-84q^{4}x-18q^{2}x^2\)
11. \(-8s^{6}-40s^{5}-50s^{4}\)
12. \(3s^{7}+30s^{6}+75s^{5}\)

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

Verbetersleutel

1. \(-6s^{7}+6s^{5}=-6s^{5}(s^2-1)=-6s^{5}(s+1)(s-1)\)
2. \(-6a^{5}-108a^{4}-486a^{3}=-6a^{3}(a^2+18a+81)=-6a^{3}(a+9)^2\)
3. \(-2p^{6}-8p^{5}-8p^{4}=-2p^{4}(p^2+4p+4)=-2p^{4}(p+2)^2\)
4. \(2x^{7}-32x^{5}=2x^{5}(x^2-16)=2x^{5}(x-4)(x+4)\)
5. \(45b^{6}+30b^{5}+5b^{4}=5b^{4}(9b^{2}+6b+1)=5b^{4}(3b+1)^2\)
6. \(216y^{8}+72y^{5}+6y^{2}=6y^{2}(36y^{6}+12y^3+1)=6y^{2}(6y^3+1)^2\)
7. \(-48a^{4}-24a^{3}-3a^{2}=-3a^{2}(16a^{2}+8a+1)=-3a^{2}(4a+1)^2\)
8. \(-54p^{12}-36p^{7}y-6p^{2}y^2=-6p^{2}(9p^{10}+6p^5y+y^2)=-6p^{2}(3p^5+y)^2\)
9. \(27b^{7}+144b^{6}+192b^{5}=3b^{5}(9b^{2}+48b+64)=3b^{5}(3b+8)^2\)
10. \(-98q^{6}-84q^{4}x-18q^{2}x^2=-2q^{2}(49q^{4}+42q^2x+9x^2)=-2q^{2}(7q^2+3x)^2\)
11. \(-8s^{6}-40s^{5}-50s^{4}=-2s^{4}(4s^{2}+20s+25)=-2s^{4}(2s+5)^2\)
12. \(3s^{7}+30s^{6}+75s^{5}=3s^{5}(s^2+10s+25)=3s^{5}(s+5)^2\)