Ontbinden in factoren (2)

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

1. \(-96p^{7}-48p^{6}-6p^{5}\)
2. \(-49a^{13}-84a^{8}x-36a^{3}x^2\)
3. \(50x^{6}+120x^{5}+72x^{4}\)
4. \(18p^{17}-2p^{3}\)
5. \(-50q^{15}+140q^{10}x-98q^{5}x^2\)
6. \(x^{5}-25x^{3}\)
7. \(-180x^{5}+300x^{4}-125x^{3}\)
8. \(6s^{6}+12s^{5}+6s^{4}\)
9. \(-9p^{6}-24p^{5}-16p^{4}\)
10. \(108s^{10}+180s^{7}+75s^{4}\)
11. \(-20y^{14}-100y^{9}-125y^{4}\)
12. \(96y^{6}-144y^{5}+54y^{4}\)

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

Verbetersleutel

1. \(-96p^{7}-48p^{6}-6p^{5}=-6p^{5}(16p^{2}+8p+1)=-6p^{5}(4p+1)^2\)
2. \(-49a^{13}-84a^{8}x-36a^{3}x^2=-a^{3}(49a^{10}+84a^5x+36x^2)=-a^{3}(7a^5+6x)^2\)
3. \(50x^{6}+120x^{5}+72x^{4}=2x^{4}(25x^{2}+60x+36)=2x^{4}(5x+6)^2\)
4. \(18p^{17}-2p^{3}=2p^{3}(9p^{14}-1)=2p^{3}(3p^7+1)(3p^7-1)\)
5. \(-50q^{15}+140q^{10}x-98q^{5}x^2=-2q^{5}(25q^{10}-70q^5x+49x^2)=-2q^{5}(5q^5-7x)^2\)
6. \(x^{5}-25x^{3}=x^{3}(x^2-25)=x^{3}(x+5)(x-5)\)
7. \(-180x^{5}+300x^{4}-125x^{3}=-5x^{3}(36x^{2}-60x+25)=-5x^{3}(6x-5)^2\)
8. \(6s^{6}+12s^{5}+6s^{4}=6s^{4}(s^2+2s+1)=6s^{4}(s+1)^2\)
9. \(-9p^{6}-24p^{5}-16p^{4}=-p^{4}(9p^{2}+24p+16)=-p^{4}(3p+4)^2\)
10. \(108s^{10}+180s^{7}+75s^{4}=3s^{4}(36s^{6}+60s^3+25)=3s^{4}(6s^3+5)^2\)
11. \(-20y^{14}-100y^{9}-125y^{4}=-5y^{4}(4y^{10}+20y^5+25)=-5y^{4}(2y^5+5)^2\)
12. \(96y^{6}-144y^{5}+54y^{4}=6y^{4}(16y^{2}-24y+9)=6y^{4}(4y-3)^2\)