Ontbinden in factoren (2)

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

1. \(-25q^{4}+q^{2}\)
2. \(-s^{5}+36s^{3}\)
3. \(2a^{6}-128a^{4}\)
4. \(s^{5}-6s^{4}+9s^{3}\)
5. \(-12b^{15}-12b^{10}-3b^{5}\)
6. \(128y^{10}-224y^{6}+98y^{2}\)
7. \(18y^{11}-8y^{3}\)
8. \(6q^{6}-48q^{5}+96q^{4}\)
9. \(5b^{5}+90b^{4}+405b^{3}\)
10. \(-54p^{10}-144p^{6}y-96p^{2}y^2\)
11. \(-q^{5}+4q^{4}-4q^{3}\)
12. \(-192q^{14}+240q^{9}y-75q^{4}y^2\)

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

Verbetersleutel

1. \(-25q^{4}+q^{2}=-q^{2}(25q^{2}-1)=-q^{2}(5q+1)(5q-1)\)
2. \(-s^{5}+36s^{3}=-s^{3}(s^2-36)=-s^{3}(s+6)(s-6)\)
3. \(2a^{6}-128a^{4}=2a^{4}(a^2-64)=2a^{4}(a-8)(a+8)\)
4. \(s^{5}-6s^{4}+9s^{3}=s^{3}(s^2-6s+9)=s^{3}(s-3)^2\)
5. \(-12b^{15}-12b^{10}-3b^{5}=-3b^{5}(4b^{10}+4b^5+1)=-3b^{5}(2b^5+1)^2\)
6. \(128y^{10}-224y^{6}+98y^{2}=2y^{2}(64y^{8}-112y^4+49)=2y^{2}(8y^4-7)^2\)
7. \(18y^{11}-8y^{3}=2y^{3}(9y^{8}-4)=2y^{3}(3y^4+2)(3y^4-2)\)
8. \(6q^{6}-48q^{5}+96q^{4}=6q^{4}(q^2-8q+16)=6q^{4}(q-4)^2\)
9. \(5b^{5}+90b^{4}+405b^{3}=5b^{3}(b^2+18b+81)=5b^{3}(b+9)^2\)
10. \(-54p^{10}-144p^{6}y-96p^{2}y^2=-6p^{2}(9p^{8}+24p^4y+16y^2)=-6p^{2}(3p^4+4y)^2\)
11. \(-q^{5}+4q^{4}-4q^{3}=-q^{3}(q^2-4q+4)=-q^{3}(q-2)^2\)
12. \(-192q^{14}+240q^{9}y-75q^{4}y^2=-3q^{4}(64q^{10}-80q^5y+25y^2)=-3q^{4}(8q^5-5y)^2\)