Ontbinden in factoren (2)

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

1. \(-6a^{5}+12a^{4}-6a^{3}\)
2. \(-96x^{17}+150x^{5}\)
3. \(150x^{6}+60x^{4}+6x^{2}\)
4. \(-24x^{5}+294x^{3}\)
5. \(-320q^{10}-80q^{6}y-5q^{2}y^2\)
6. \(216q^{9}+72q^{7}+6q^{5}\)
7. \(384s^{7}-672s^{6}+294s^{5}\)
8. \(-384x^{11}-288x^{7}-54x^{3}\)
9. \(-384q^{13}+480q^{8}-150q^{3}\)
10. \(72y^{10}+24y^{7}+2y^{4}\)
11. \(8s^{9}-2s^{3}\)
12. \(-125a^{8}+350a^{5}y-245a^{2}y^2\)

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

Verbetersleutel

1. \(-6a^{5}+12a^{4}-6a^{3}=-6a^{3}(a^2-2a+1)=-6a^{3}(a-1)^2\)
2. \(-96x^{17}+150x^{5}=-6x^{5}(16x^{12}-25)=-6x^{5}(4x^6+5)(4x^6-5)\)
3. \(150x^{6}+60x^{4}+6x^{2}=6x^{2}(25x^{4}+10x^2+1)=6x^{2}(5x^2+1)^2\)
4. \(-24x^{5}+294x^{3}=-6x^{3}(4x^{2}-49)=-6x^{3}(2x+7)(2x-7)\)
5. \(-320q^{10}-80q^{6}y-5q^{2}y^2=-5q^{2}(64q^{8}+16q^4y+y^2)=-5q^{2}(8q^4+y)^2\)
6. \(216q^{9}+72q^{7}+6q^{5}=6q^{5}(36q^{4}+12q^2+1)=6q^{5}(6q^2+1)^2\)
7. \(384s^{7}-672s^{6}+294s^{5}=6s^{5}(64s^{2}-112s+49)=6s^{5}(8s-7)^2\)
8. \(-384x^{11}-288x^{7}-54x^{3}=-6x^{3}(64x^{8}+48x^4+9)=-6x^{3}(8x^4+3)^2\)
9. \(-384q^{13}+480q^{8}-150q^{3}=-6q^{3}(64q^{10}-80q^5+25)=-6q^{3}(8q^5-5)^2\)
10. \(72y^{10}+24y^{7}+2y^{4}=2y^{4}(36y^{6}+12y^3+1)=2y^{4}(6y^3+1)^2\)
11. \(8s^{9}-2s^{3}=2s^{3}(4s^{6}-1)=2s^{3}(2s^3+1)(2s^3-1)\)
12. \(-125a^{8}+350a^{5}y-245a^{2}y^2=-5a^{2}(25a^{6}-70a^3y+49y^2)=-5a^{2}(5a^3-7y)^2\)