Ontbinden in factoren (2)

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

1. \(-45p^{6}-210p^{5}-245p^{4}\)
2. \(-245q^{12}-280q^{7}y-80q^{2}y^2\)
3. \(-2s^{6}+20s^{5}-50s^{4}\)
4. \(s^{6}-25s^{4}\)
5. \(-2y^{6}+8y^{5}-8y^{4}\)
6. \(-b^{5}-18b^{4}-81b^{3}\)
7. \(245b^{4}+630b^{3}+405b^{2}\)
8. \(-48p^{5}-72p^{4}-27p^{3}\)
9. \(-27s^{11}+3s^{3}\)
10. \(3a^{4}-12a^{3}+12a^{2}\)
11. \(150q^{15}-96q^{3}\)
12. \(108a^{12}+36a^{7}+3a^{2}\)

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

Verbetersleutel

1. \(-45p^{6}-210p^{5}-245p^{4}=-5p^{4}(9p^{2}+42p+49)=-5p^{4}(3p+7)^2\)
2. \(-245q^{12}-280q^{7}y-80q^{2}y^2=-5q^{2}(49q^{10}+56q^5y+16y^2)=-5q^{2}(7q^5+4y)^2\)
3. \(-2s^{6}+20s^{5}-50s^{4}=-2s^{4}(s^2-10s+25)=-2s^{4}(s-5)^2\)
4. \(s^{6}-25s^{4}=s^{4}(s^2-25)=s^{4}(s+5)(s-5)\)
5. \(-2y^{6}+8y^{5}-8y^{4}=-2y^{4}(y^2-4y+4)=-2y^{4}(y-2)^2\)
6. \(-b^{5}-18b^{4}-81b^{3}=-b^{3}(b^2+18b+81)=-b^{3}(b+9)^2\)
7. \(245b^{4}+630b^{3}+405b^{2}=5b^{2}(49b^{2}+126b+81)=5b^{2}(7b+9)^2\)
8. \(-48p^{5}-72p^{4}-27p^{3}=-3p^{3}(16p^{2}+24p+9)=-3p^{3}(4p+3)^2\)
9. \(-27s^{11}+3s^{3}=-3s^{3}(9s^{8}-1)=-3s^{3}(3s^4+1)(3s^4-1)\)
10. \(3a^{4}-12a^{3}+12a^{2}=3a^{2}(a^2-4a+4)=3a^{2}(a-2)^2\)
11. \(150q^{15}-96q^{3}=6q^{3}(25q^{12}-16)=6q^{3}(5q^6+4)(5q^6-4)\)
12. \(108a^{12}+36a^{7}+3a^{2}=3a^{2}(36a^{10}+12a^5+1)=3a^{2}(6a^5+1)^2\)