Ontbinden in factoren (2)

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

1. \(-50s^{7}+8s^{5}\)
2. \(-150a^{4}+24a^{2}\)
3. \(6q^{5}-216q^{3}\)
4. \(-12q^{7}-84q^{6}-147q^{5}\)
5. \(-216b^{8}+360b^{6}-150b^{4}\)
6. \(-32a^{6}-16a^{5}-2a^{4}\)
7. \(25p^{7}-p^{5}\)
8. \(108q^{9}+36q^{6}+3q^{3}\)
9. \(-6s^{5}+60s^{4}-150s^{3}\)
10. \(-45q^{6}+5q^{2}\)
11. \(-20a^{14}-20a^{9}y-5a^{4}y^2\)
12. \(-6a^{5}+294a^{3}\)

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

Verbetersleutel

1. \(-50s^{7}+8s^{5}=-2s^{5}(25s^{2}-4)=-2s^{5}(5s+2)(5s-2)\)
2. \(-150a^{4}+24a^{2}=-6a^{2}(25a^{2}-4)=-6a^{2}(5a+2)(5a-2)\)
3. \(6q^{5}-216q^{3}=6q^{3}(q^2-36)=6q^{3}(q+6)(q-6)\)
4. \(-12q^{7}-84q^{6}-147q^{5}=-3q^{5}(4q^{2}+28q+49)=-3q^{5}(2q+7)^2\)
5. \(-216b^{8}+360b^{6}-150b^{4}=-6b^{4}(36b^{4}-60b^2+25)=-6b^{4}(6b^2-5)^2\)
6. \(-32a^{6}-16a^{5}-2a^{4}=-2a^{4}(16a^{2}+8a+1)=-2a^{4}(4a+1)^2\)
7. \(25p^{7}-p^{5}=p^{5}(25p^{2}-1)=p^{5}(5p+1)(5p-1)\)
8. \(108q^{9}+36q^{6}+3q^{3}=3q^{3}(36q^{6}+12q^3+1)=3q^{3}(6q^3+1)^2\)
9. \(-6s^{5}+60s^{4}-150s^{3}=-6s^{3}(s^2-10s+25)=-6s^{3}(s-5)^2\)
10. \(-45q^{6}+5q^{2}=-5q^{2}(9q^{4}-1)=-5q^{2}(3q^2+1)(3q^2-1)\)
11. \(-20a^{14}-20a^{9}y-5a^{4}y^2=-5a^{4}(4a^{10}+4a^5y+y^2)=-5a^{4}(2a^5+y)^2\)
12. \(-6a^{5}+294a^{3}=-6a^{3}(a^2-49)=-6a^{3}(a-7)(a+7)\)