Ontbinden in factoren (2)

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

1. \(-6x^{5}+60x^{4}-150x^{3}\)
2. \(-36s^{6}+60s^{4}y-25s^{2}y^2\)
3. \(-32x^{10}-80x^{7}-50x^{4}\)
4. \(64y^{4}+16y^{3}+y^{2}\)
5. \(-y^{6}-8y^{5}-16y^{4}\)
6. \(-p^{6}+16p^{4}\)
7. \(-5q^{5}+40q^{4}-80q^{3}\)
8. \(-b^{5}+49b^{3}\)
9. \(-180q^{9}+300q^{6}-125q^{3}\)
10. \(-16b^{12}+9b^{2}\)
11. \(-54y^{19}+150y^{5}\)
12. \(-64a^{11}-16a^{7}-a^{3}\)

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

Verbetersleutel

1. \(-6x^{5}+60x^{4}-150x^{3}=-6x^{3}(x^2-10x+25)=-6x^{3}(x-5)^2\)
2. \(-36s^{6}+60s^{4}y-25s^{2}y^2=-s^{2}(36s^{4}-60s^2y+25y^2)=-s^{2}(6s^2-5y)^2\)
3. \(-32x^{10}-80x^{7}-50x^{4}=-2x^{4}(16x^{6}+40x^3+25)=-2x^{4}(4x^3+5)^2\)
4. \(64y^{4}+16y^{3}+y^{2}=y^{2}(64y^{2}+16y+1)=y^{2}(8y+1)^2\)
5. \(-y^{6}-8y^{5}-16y^{4}=-y^{4}(y^2+8y+16)=-y^{4}(y+4)^2\)
6. \(-p^{6}+16p^{4}=-p^{4}(p^2-16)=-p^{4}(p-4)(p+4)\)
7. \(-5q^{5}+40q^{4}-80q^{3}=-5q^{3}(q^2-8q+16)=-5q^{3}(q-4)^2\)
8. \(-b^{5}+49b^{3}=-b^{3}(b^2-49)=-b^{3}(b-7)(b+7)\)
9. \(-180q^{9}+300q^{6}-125q^{3}=-5q^{3}(36q^{6}-60q^3+25)=-5q^{3}(6q^3-5)^2\)
10. \(-16b^{12}+9b^{2}=-b^{2}(16b^{10}-9)=-b^{2}(4b^5+3)(4b^5-3)\)
11. \(-54y^{19}+150y^{5}=-6y^{5}(9y^{14}-25)=-6y^{5}(3y^7+5)(3y^7-5)\)
12. \(-64a^{11}-16a^{7}-a^{3}=-a^{3}(64a^{8}+16a^4+1)=-a^{3}(8a^4+1)^2\)