Ontbinden in factoren (2)

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

1. \(-3p^{7}-36p^{6}-108p^{5}\)
2. \(2p^{6}-8p^{4}\)
3. \(216s^{5}+72s^{4}+6s^{3}\)
4. \(-128b^{7}+224b^{5}q-98b^{3}q^2\)
5. \(-80q^{17}+5q^{5}\)
6. \(3y^{7}-108y^{5}\)
7. \(20x^{13}-125x^{3}\)
8. \(24p^{15}+24p^{10}s+6p^{5}s^2\)
9. \(-98s^{9}-84s^{7}x-18s^{5}x^2\)
10. \(-24q^{15}-24q^{10}-6q^{5}\)
11. \(384a^{10}+96a^{7}y+6a^{4}y^2\)
12. \(245x^{6}-630x^{5}+405x^{4}\)

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

Verbetersleutel

1. \(-3p^{7}-36p^{6}-108p^{5}=-3p^{5}(p^2+12p+36)=-3p^{5}(p+6)^2\)
2. \(2p^{6}-8p^{4}=2p^{4}(p^2-4)=2p^{4}(p-2)(p+2)\)
3. \(216s^{5}+72s^{4}+6s^{3}=6s^{3}(36s^{2}+12s+1)=6s^{3}(6s+1)^2\)
4. \(-128b^{7}+224b^{5}q-98b^{3}q^2=-2b^{3}(64b^{4}-112b^2q+49q^2)=-2b^{3}(8b^2-7q)^2\)
5. \(-80q^{17}+5q^{5}=-5q^{5}(16q^{12}-1)=-5q^{5}(4q^6+1)(4q^6-1)\)
6. \(3y^{7}-108y^{5}=3y^{5}(y^2-36)=3y^{5}(y-6)(y+6)\)
7. \(20x^{13}-125x^{3}=5x^{3}(4x^{10}-25)=5x^{3}(2x^5+5)(2x^5-5)\)
8. \(24p^{15}+24p^{10}s+6p^{5}s^2=6p^{5}(4p^{10}+4p^5s+s^2)=6p^{5}(2p^5+s)^2\)
9. \(-98s^{9}-84s^{7}x-18s^{5}x^2=-2s^{5}(49s^{4}+42s^2x+9x^2)=-2s^{5}(7s^2+3x)^2\)
10. \(-24q^{15}-24q^{10}-6q^{5}=-6q^{5}(4q^{10}+4q^5+1)=-6q^{5}(2q^5+1)^2\)
11. \(384a^{10}+96a^{7}y+6a^{4}y^2=6a^{4}(64a^{6}+16a^3y+y^2)=6a^{4}(8a^3+y)^2\)
12. \(245x^{6}-630x^{5}+405x^{4}=5x^{4}(49x^{2}-126x+81)=5x^{4}(7x-9)^2\)