Ontbinden in factoren (2)

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

1. \(98y^{5}-168y^{4}+72y^{3}\)
2. \(a^{4}+12a^{3}+36a^{2}\)
3. \(-20b^{7}-140b^{6}-245b^{5}\)
4. \(-75q^{7}+270q^{6}-243q^{5}\)
5. \(72a^{7}-120a^{6}+50a^{5}\)
6. \(-125y^{5}+450y^{4}-405y^{3}\)
7. \(320a^{8}+80a^{6}s+5a^{4}s^2\)
8. \(y^{7}-14y^{6}+49y^{5}\)
9. \(3p^{6}-192p^{4}\)
10. \(-25a^{9}-10a^{6}q-a^{3}q^2\)
11. \(-6b^{6}+96b^{4}\)
12. \(6p^{7}+108p^{6}+486p^{5}\)

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

Verbetersleutel

1. \(98y^{5}-168y^{4}+72y^{3}=2y^{3}(49y^{2}-84y+36)=2y^{3}(7y-6)^2\)
2. \(a^{4}+12a^{3}+36a^{2}=a^{2}(a^2+12a+36)=a^{2}(a+6)^2\)
3. \(-20b^{7}-140b^{6}-245b^{5}=-5b^{5}(4b^{2}+28b+49)=-5b^{5}(2b+7)^2\)
4. \(-75q^{7}+270q^{6}-243q^{5}=-3q^{5}(25q^{2}-90q+81)=-3q^{5}(5q-9)^2\)
5. \(72a^{7}-120a^{6}+50a^{5}=2a^{5}(36a^{2}-60a+25)=2a^{5}(6a-5)^2\)
6. \(-125y^{5}+450y^{4}-405y^{3}=-5y^{3}(25y^{2}-90y+81)=-5y^{3}(5y-9)^2\)
7. \(320a^{8}+80a^{6}s+5a^{4}s^2=5a^{4}(64a^{4}+16a^2s+s^2)=5a^{4}(8a^2+s)^2\)
8. \(y^{7}-14y^{6}+49y^{5}=y^{5}(y^2-14y+49)=y^{5}(y-7)^2\)
9. \(3p^{6}-192p^{4}=3p^{4}(p^2-64)=3p^{4}(p-8)(p+8)\)
10. \(-25a^{9}-10a^{6}q-a^{3}q^2=-a^{3}(25a^{6}+10a^3q+q^2)=-a^{3}(5a^3+q)^2\)
11. \(-6b^{6}+96b^{4}=-6b^{4}(b^2-16)=-6b^{4}(b+4)(b-4)\)
12. \(6p^{7}+108p^{6}+486p^{5}=6p^{5}(p^2+18p+81)=6p^{5}(p+9)^2\)