Ontbinden in factoren (2)

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

1. \(-2b^{6}-32b^{5}-128b^{4}\)
2. \(125x^{10}-80x^{2}\)
3. \(147s^{4}-84s^{3}+12s^{2}\)
4. \(-6q^{5}-72q^{4}-216q^{3}\)
5. \(-6b^{4}+54b^{2}\)
6. \(-96y^{10}+144y^{7}-54y^{4}\)
7. \(72q^{4}+168q^{3}+98q^{2}\)
8. \(-2b^{6}+18b^{4}\)
9. \(108x^{8}+36x^{6}+3x^{4}\)
10. \(-49a^{10}-14a^{6}y-a^{2}y^2\)
11. \(108x^{8}+180x^{5}+75x^{2}\)
12. \(-150a^{13}+420a^{9}y-294a^{5}y^2\)

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

Verbetersleutel

1. \(-2b^{6}-32b^{5}-128b^{4}=-2b^{4}(b^2+16b+64)=-2b^{4}(b+8)^2\)
2. \(125x^{10}-80x^{2}=5x^{2}(25x^{8}-16)=5x^{2}(5x^4+4)(5x^4-4)\)
3. \(147s^{4}-84s^{3}+12s^{2}=3s^{2}(49s^{2}-28s+4)=3s^{2}(7s-2)^2\)
4. \(-6q^{5}-72q^{4}-216q^{3}=-6q^{3}(q^2+12q+36)=-6q^{3}(q+6)^2\)
5. \(-6b^{4}+54b^{2}=-6b^{2}(b^2-9)=-6b^{2}(b-3)(b+3)\)
6. \(-96y^{10}+144y^{7}-54y^{4}=-6y^{4}(16y^{6}-24y^3+9)=-6y^{4}(4y^3-3)^2\)
7. \(72q^{4}+168q^{3}+98q^{2}=2q^{2}(36q^{2}+84q+49)=2q^{2}(6q+7)^2\)
8. \(-2b^{6}+18b^{4}=-2b^{4}(b^2-9)=-2b^{4}(b-3)(b+3)\)
9. \(108x^{8}+36x^{6}+3x^{4}=3x^{4}(36x^{4}+12x^2+1)=3x^{4}(6x^2+1)^2\)
10. \(-49a^{10}-14a^{6}y-a^{2}y^2=-a^{2}(49a^{8}+14a^4y+y^2)=-a^{2}(7a^4+y)^2\)
11. \(108x^{8}+180x^{5}+75x^{2}=3x^{2}(36x^{6}+60x^3+25)=3x^{2}(6x^3+5)^2\)
12. \(-150a^{13}+420a^{9}y-294a^{5}y^2=-6a^{5}(25a^{8}-70a^4y+49y^2)=-6a^{5}(5a^4-7y)^2\)