Ontbinden in factoren (2)

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

1. \(216s^{7}-360s^{6}+150s^{5}\)
2. \(-180b^{9}-60b^{6}p-5b^{3}p^2\)
3. \(9q^{11}-30q^{7}s+25q^{3}s^2\)
4. \(6s^{7}-54s^{5}\)
5. \(6q^{5}-96q^{4}+384q^{3}\)
6. \(6y^{4}-36y^{3}+54y^{2}\)
7. \(3s^{5}-192s^{3}\)
8. \(75q^{6}-108q^{2}\)
9. \(-320q^{8}+400q^{6}-125q^{4}\)
10. \(32a^{6}-50a^{4}\)
11. \(80y^{5}+40y^{4}+5y^{3}\)
12. \(9q^{4}-25q^{2}\)

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

Verbetersleutel

1. \(216s^{7}-360s^{6}+150s^{5}=6s^{5}(36s^{2}-60s+25)=6s^{5}(6s-5)^2\)
2. \(-180b^{9}-60b^{6}p-5b^{3}p^2=-5b^{3}(36b^{6}+12b^3p+p^2)=-5b^{3}(6b^3+p)^2\)
3. \(9q^{11}-30q^{7}s+25q^{3}s^2=q^{3}(9q^{8}-30q^4s+25s^2)=q^{3}(3q^4-5s)^2\)
4. \(6s^{7}-54s^{5}=6s^{5}(s^2-9)=6s^{5}(s+3)(s-3)\)
5. \(6q^{5}-96q^{4}+384q^{3}=6q^{3}(q^2-16q+64)=6q^{3}(q-8)^2\)
6. \(6y^{4}-36y^{3}+54y^{2}=6y^{2}(y^2-6y+9)=6y^{2}(y-3)^2\)
7. \(3s^{5}-192s^{3}=3s^{3}(s^2-64)=3s^{3}(s+8)(s-8)\)
8. \(75q^{6}-108q^{2}=3q^{2}(25q^{4}-36)=3q^{2}(5q^2+6)(5q^2-6)\)
9. \(-320q^{8}+400q^{6}-125q^{4}=-5q^{4}(64q^{4}-80q^2+25)=-5q^{4}(8q^2-5)^2\)
10. \(32a^{6}-50a^{4}=2a^{4}(16a^{2}-25)=2a^{4}(4a+5)(4a-5)\)
11. \(80y^{5}+40y^{4}+5y^{3}=5y^{3}(16y^{2}+8y+1)=5y^{3}(4y+1)^2\)
12. \(9q^{4}-25q^{2}=q^{2}(9q^{2}-25)=q^{2}(3q+5)(3q-5)\)