Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(-245s^{4}-210s^{3}-45s^{2}\)
2. \(36a^{9}+60a^{6}+25a^{3}\)
3. \(80p^{10}-125p^{4}\)
4. \(45a^{5}-240a^{4}+320a^{3}\)
5. \(-3x^{7}+12x^{6}-12x^{5}\)
6. \(245y^{14}+70y^{9}+5y^{4}\)
7. \(180p^{4}-125p^{2}\)
8. \(-96x^{7}+54x^{5}\)
9. \(49p^{15}-84p^{10}q+36p^{5}q^2\)
10. \(-8b^{4}-8b^{3}-2b^{2}\)
11. \(245a^{4}-420a^{3}+180a^{2}\)
12. \(-20s^{7}-20s^{5}y-5s^{3}y^2\)

---

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

Verbetersleutel

1. \(-245s^{4}-210s^{3}-45s^{2}=-5s^{2}(49s^{2}+42s+9)=-5s^{2}(7s+3)^2\)
2. \(36a^{9}+60a^{6}+25a^{3}=a^{3}(36a^{6}+60a^3+25)=a^{3}(6a^3+5)^2\)
3. \(80p^{10}-125p^{4}=5p^{4}(16p^{6}-25)=5p^{4}(4p^3+5)(4p^3-5)\)
4. \(45a^{5}-240a^{4}+320a^{3}=5a^{3}(9a^{2}-48a+64)=5a^{3}(3a-8)^2\)
5. \(-3x^{7}+12x^{6}-12x^{5}=-3x^{5}(x^2-4x+4)=-3x^{5}(x-2)^2\)
6. \(245y^{14}+70y^{9}+5y^{4}=5y^{4}(49y^{10}+14y^5+1)=5y^{4}(7y^5+1)^2\)
7. \(180p^{4}-125p^{2}=5p^{2}(36p^{2}-25)=5p^{2}(6p+5)(6p-5)\)
8. \(-96x^{7}+54x^{5}=-6x^{5}(16x^{2}-9)=-6x^{5}(4x+3)(4x-3)\)
9. \(49p^{15}-84p^{10}q+36p^{5}q^2=p^{5}(49p^{10}-84p^5q+36q^2)=p^{5}(7p^5-6q)^2\)
10. \(-8b^{4}-8b^{3}-2b^{2}=-2b^{2}(4b^{2}+4b+1)=-2b^{2}(2b+1)^2\)
11. \(245a^{4}-420a^{3}+180a^{2}=5a^{2}(49a^{2}-84a+36)=5a^{2}(7a-6)^2\)
12. \(-20s^{7}-20s^{5}y-5s^{3}y^2=-5s^{3}(4s^{4}+4s^2y+y^2)=-5s^{3}(2s^2+y)^2\)