Ontbinden in factoren (2)

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

1. \(49s^{4}+14s^{3}+s^{2}\)
2. \(24p^{11}+120p^{8}y+150p^{5}y^2\)
3. \(-96b^{7}+6b^{5}\)
4. \(5p^{6}-50p^{5}+125p^{4}\)
5. \(2p^{7}-2p^{5}\)
6. \(3s^{7}+54s^{6}+243s^{5}\)
7. \(-20a^{13}-20a^{8}s-5a^{3}s^2\)
8. \(3q^{5}+6q^{4}+3q^{3}\)
9. \(3b^{7}+24b^{6}+48b^{5}\)
10. \(245p^{7}+70p^{6}+5p^{5}\)
11. \(36y^{10}-y^{2}\)
12. \(32s^{7}-2s^{5}\)

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

Verbetersleutel

1. \(49s^{4}+14s^{3}+s^{2}=s^{2}(49s^{2}+14s+1)=s^{2}(7s+1)^2\)
2. \(24p^{11}+120p^{8}y+150p^{5}y^2=6p^{5}(4p^{6}+20p^3y+25y^2)=6p^{5}(2p^3+5y)^2\)
3. \(-96b^{7}+6b^{5}=-6b^{5}(16b^{2}-1)=-6b^{5}(4b+1)(4b-1)\)
4. \(5p^{6}-50p^{5}+125p^{4}=5p^{4}(p^2-10p+25)=5p^{4}(p-5)^2\)
5. \(2p^{7}-2p^{5}=2p^{5}(p^2-1)=2p^{5}(p+1)(p-1)\)
6. \(3s^{7}+54s^{6}+243s^{5}=3s^{5}(s^2+18s+81)=3s^{5}(s+9)^2\)
7. \(-20a^{13}-20a^{8}s-5a^{3}s^2=-5a^{3}(4a^{10}+4a^5s+s^2)=-5a^{3}(2a^5+s)^2\)
8. \(3q^{5}+6q^{4}+3q^{3}=3q^{3}(q^2+2q+1)=3q^{3}(q+1)^2\)
9. \(3b^{7}+24b^{6}+48b^{5}=3b^{5}(b^2+8b+16)=3b^{5}(b+4)^2\)
10. \(245p^{7}+70p^{6}+5p^{5}=5p^{5}(49p^{2}+14p+1)=5p^{5}(7p+1)^2\)
11. \(36y^{10}-y^{2}=y^{2}(36y^{8}-1)=y^{2}(6y^4+1)(6y^4-1)\)
12. \(32s^{7}-2s^{5}=2s^{5}(16s^{2}-1)=2s^{5}(4s+1)(4s-1)\)