Ontbinden in factoren (2)

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

1. \(-3x^{4}+192x^{2}\)
2. \(6b^{7}-150b^{5}\)
3. \(-36x^{6}-12x^{4}y-x^{2}y^2\)
4. \(-180x^{19}+125x^{5}\)
5. \(-6x^{5}+384x^{3}\)
6. \(-72y^{7}-24y^{5}-2y^{3}\)
7. \(-2p^{5}+50p^{3}\)
8. \(2p^{7}-24p^{6}+72p^{5}\)
9. \(-192p^{6}-336p^{5}-147p^{4}\)
10. \(-2x^{7}+8x^{6}-8x^{5}\)
11. \(6y^{6}-24y^{4}\)
12. \(-54s^{12}+180s^{7}-150s^{2}\)

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

Verbetersleutel

1. \(-3x^{4}+192x^{2}=-3x^{2}(x^2-64)=-3x^{2}(x+8)(x-8)\)
2. \(6b^{7}-150b^{5}=6b^{5}(b^2-25)=6b^{5}(b+5)(b-5)\)
3. \(-36x^{6}-12x^{4}y-x^{2}y^2=-x^{2}(36x^{4}+12x^2y+y^2)=-x^{2}(6x^2+y)^2\)
4. \(-180x^{19}+125x^{5}=-5x^{5}(36x^{14}-25)=-5x^{5}(6x^7+5)(6x^7-5)\)
5. \(-6x^{5}+384x^{3}=-6x^{3}(x^2-64)=-6x^{3}(x+8)(x-8)\)
6. \(-72y^{7}-24y^{5}-2y^{3}=-2y^{3}(36y^{4}+12y^2+1)=-2y^{3}(6y^2+1)^2\)
7. \(-2p^{5}+50p^{3}=-2p^{3}(p^2-25)=-2p^{3}(p-5)(p+5)\)
8. \(2p^{7}-24p^{6}+72p^{5}=2p^{5}(p^2-12p+36)=2p^{5}(p-6)^2\)
9. \(-192p^{6}-336p^{5}-147p^{4}=-3p^{4}(64p^{2}+112p+49)=-3p^{4}(8p+7)^2\)
10. \(-2x^{7}+8x^{6}-8x^{5}=-2x^{5}(x^2-4x+4)=-2x^{5}(x-2)^2\)
11. \(6y^{6}-24y^{4}=6y^{4}(y^2-4)=6y^{4}(y-2)(y+2)\)
12. \(-54s^{12}+180s^{7}-150s^{2}=-6s^{2}(9s^{10}-30s^5+25)=-6s^{2}(3s^5-5)^2\)