Ontbinden in factoren (2)

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

1. \(-125q^{13}+350q^{8}s-245q^{3}s^2\)
2. \(-147y^{4}-126y^{3}-27y^{2}\)
3. \(-25q^{13}+49q^{3}\)
4. \(48a^{20}-3a^{4}\)
5. \(5a^{4}-90a^{3}+405a^{2}\)
6. \(6b^{4}-84b^{3}+294b^{2}\)
7. \(-80b^{13}+280b^{8}-245b^{3}\)
8. \(45b^{6}-150b^{4}+125b^{2}\)
9. \(5q^{4}+90q^{3}+405q^{2}\)
10. \(-150a^{6}+216a^{4}\)
11. \(180y^{5}+60y^{4}+5y^{3}\)
12. \(-150p^{10}+240p^{6}s-96p^{2}s^2\)

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

Verbetersleutel

1. \(-125q^{13}+350q^{8}s-245q^{3}s^2=-5q^{3}(25q^{10}-70q^5s+49s^2)=-5q^{3}(5q^5-7s)^2\)
2. \(-147y^{4}-126y^{3}-27y^{2}=-3y^{2}(49y^{2}+42y+9)=-3y^{2}(7y+3)^2\)
3. \(-25q^{13}+49q^{3}=-q^{3}(25q^{10}-49)=-q^{3}(5q^5+7)(5q^5-7)\)
4. \(48a^{20}-3a^{4}=3a^{4}(16a^{16}-1)=3a^{4}(4a^8+1)(4a^8-1)\)
5. \(5a^{4}-90a^{3}+405a^{2}=5a^{2}(a^2-18a+81)=5a^{2}(a-9)^2\)
6. \(6b^{4}-84b^{3}+294b^{2}=6b^{2}(b^2-14b+49)=6b^{2}(b-7)^2\)
7. \(-80b^{13}+280b^{8}-245b^{3}=-5b^{3}(16b^{10}-56b^5+49)=-5b^{3}(4b^5-7)^2\)
8. \(45b^{6}-150b^{4}+125b^{2}=5b^{2}(9b^{4}-30b^2+25)=5b^{2}(3b^2-5)^2\)
9. \(5q^{4}+90q^{3}+405q^{2}=5q^{2}(q^2+18q+81)=5q^{2}(q+9)^2\)
10. \(-150a^{6}+216a^{4}=-6a^{4}(25a^{2}-36)=-6a^{4}(5a+6)(5a-6)\)
11. \(180y^{5}+60y^{4}+5y^{3}=5y^{3}(36y^{2}+12y+1)=5y^{3}(6y+1)^2\)
12. \(-150p^{10}+240p^{6}s-96p^{2}s^2=-6p^{2}(25p^{8}-40p^4s+16s^2)=-6p^{2}(5p^4-4s)^2\)