Ontbinden in factoren (2)

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

1. \(-20y^{14}-100y^{9}-125y^{4}\)
2. \(-6a^{6}-60a^{5}-150a^{4}\)
3. \(25a^{10}+10a^{6}x+a^{2}x^2\)
4. \(75y^{5}+180y^{4}+108y^{3}\)
5. \(-y^{6}-6y^{5}-9y^{4}\)
6. \(108b^{11}-75b^{3}\)
7. \(-12q^{16}+147q^{4}\)
8. \(-80s^{12}+120s^{8}y-45s^{4}y^2\)
9. \(18s^{11}-60s^{8}+50s^{5}\)
10. \(-9q^{7}+12q^{5}x-4q^{3}x^2\)
11. \(-p^{6}+p^{4}\)
12. \(2p^{7}+12p^{6}+18p^{5}\)

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

Verbetersleutel

1. \(-20y^{14}-100y^{9}-125y^{4}=-5y^{4}(4y^{10}+20y^5+25)=-5y^{4}(2y^5+5)^2\)
2. \(-6a^{6}-60a^{5}-150a^{4}=-6a^{4}(a^2+10a+25)=-6a^{4}(a+5)^2\)
3. \(25a^{10}+10a^{6}x+a^{2}x^2=a^{2}(25a^{8}+10a^4x+x^2)=a^{2}(5a^4+x)^2\)
4. \(75y^{5}+180y^{4}+108y^{3}=3y^{3}(25y^{2}+60y+36)=3y^{3}(5y+6)^2\)
5. \(-y^{6}-6y^{5}-9y^{4}=-y^{4}(y^2+6y+9)=-y^{4}(y+3)^2\)
6. \(108b^{11}-75b^{3}=3b^{3}(36b^{8}-25)=3b^{3}(6b^4+5)(6b^4-5)\)
7. \(-12q^{16}+147q^{4}=-3q^{4}(4q^{12}-49)=-3q^{4}(2q^6+7)(2q^6-7)\)
8. \(-80s^{12}+120s^{8}y-45s^{4}y^2=-5s^{4}(16s^{8}-24s^4y+9y^2)=-5s^{4}(4s^4-3y)^2\)
9. \(18s^{11}-60s^{8}+50s^{5}=2s^{5}(9s^{6}-30s^3+25)=2s^{5}(3s^3-5)^2\)
10. \(-9q^{7}+12q^{5}x-4q^{3}x^2=-q^{3}(9q^{4}-12q^2x+4x^2)=-q^{3}(3q^2-2x)^2\)
11. \(-p^{6}+p^{4}=-p^{4}(p^2-1)=-p^{4}(p-1)(p+1)\)
12. \(2p^{7}+12p^{6}+18p^{5}=2p^{5}(p^2+6p+9)=2p^{5}(p+3)^2\)