Ontbinden in factoren (2)

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

1. \(27s^{4}-147s^{2}\)
2. \(-b^{5}+18b^{4}-81b^{3}\)
3. \(-96s^{15}+336s^{10}-294s^{5}\)
4. \(-25q^{7}+40q^{6}-16q^{5}\)
5. \(-150s^{7}-360s^{6}-216s^{5}\)
6. \(6x^{4}-96x^{3}+384x^{2}\)
7. \(5x^{4}-20x^{3}+20x^{2}\)
8. \(6p^{6}-216p^{4}\)
9. \(147a^{6}-84a^{4}s+12a^{2}s^2\)
10. \(16y^{7}-24y^{6}+9y^{5}\)
11. \(-2b^{5}-36b^{4}-162b^{3}\)
12. \(18x^{7}-2x^{5}\)

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

Verbetersleutel

1. \(27s^{4}-147s^{2}=3s^{2}(9s^{2}-49)=3s^{2}(3s+7)(3s-7)\)
2. \(-b^{5}+18b^{4}-81b^{3}=-b^{3}(b^2-18b+81)=-b^{3}(b-9)^2\)
3. \(-96s^{15}+336s^{10}-294s^{5}=-6s^{5}(16s^{10}-56s^5+49)=-6s^{5}(4s^5-7)^2\)
4. \(-25q^{7}+40q^{6}-16q^{5}=-q^{5}(25q^{2}-40q+16)=-q^{5}(5q-4)^2\)
5. \(-150s^{7}-360s^{6}-216s^{5}=-6s^{5}(25s^{2}+60s+36)=-6s^{5}(5s+6)^2\)
6. \(6x^{4}-96x^{3}+384x^{2}=6x^{2}(x^2-16x+64)=6x^{2}(x-8)^2\)
7. \(5x^{4}-20x^{3}+20x^{2}=5x^{2}(x^2-4x+4)=5x^{2}(x-2)^2\)
8. \(6p^{6}-216p^{4}=6p^{4}(p^2-36)=6p^{4}(p+6)(p-6)\)
9. \(147a^{6}-84a^{4}s+12a^{2}s^2=3a^{2}(49a^{4}-28a^2s+4s^2)=3a^{2}(7a^2-2s)^2\)
10. \(16y^{7}-24y^{6}+9y^{5}=y^{5}(16y^{2}-24y+9)=y^{5}(4y-3)^2\)
11. \(-2b^{5}-36b^{4}-162b^{3}=-2b^{3}(b^2+18b+81)=-2b^{3}(b+9)^2\)
12. \(18x^{7}-2x^{5}=2x^{5}(9x^{2}-1)=2x^{5}(3x+1)(3x-1)\)