Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(245y^{11}-140y^{8}+20y^{5}\)
2. \(-24p^{5}-24p^{4}-6p^{3}\)
3. \(-2a^{5}+50a^{3}\)
4. \(108q^{12}-75q^{4}\)
5. \(6a^{6}-6a^{4}\)
6. \(25a^{9}-16a^{3}\)
7. \(-12p^{4}+147p^{2}\)
8. \(-150x^{7}-120x^{6}-24x^{5}\)
9. \(245q^{4}-140q^{3}+20q^{2}\)
10. \(-54p^{10}+72p^{6}q-24p^{2}q^2\)
11. \(-32y^{14}+98y^{2}\)
12. \(-16p^{21}+25p^{5}\)

---

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

Verbetersleutel

1. \(245y^{11}-140y^{8}+20y^{5}=5y^{5}(49y^{6}-28y^3+4)=5y^{5}(7y^3-2)^2\)
2. \(-24p^{5}-24p^{4}-6p^{3}=-6p^{3}(4p^{2}+4p+1)=-6p^{3}(2p+1)^2\)
3. \(-2a^{5}+50a^{3}=-2a^{3}(a^2-25)=-2a^{3}(a+5)(a-5)\)
4. \(108q^{12}-75q^{4}=3q^{4}(36q^{8}-25)=3q^{4}(6q^4+5)(6q^4-5)\)
5. \(6a^{6}-6a^{4}=6a^{4}(a^2-1)=6a^{4}(a-1)(a+1)\)
6. \(25a^{9}-16a^{3}=a^{3}(25a^{6}-16)=a^{3}(5a^3+4)(5a^3-4)\)
7. \(-12p^{4}+147p^{2}=-3p^{2}(4p^{2}-49)=-3p^{2}(2p+7)(2p-7)\)
8. \(-150x^{7}-120x^{6}-24x^{5}=-6x^{5}(25x^{2}+20x+4)=-6x^{5}(5x+2)^2\)
9. \(245q^{4}-140q^{3}+20q^{2}=5q^{2}(49q^{2}-28q+4)=5q^{2}(7q-2)^2\)
10. \(-54p^{10}+72p^{6}q-24p^{2}q^2=-6p^{2}(9p^{8}-12p^4q+4q^2)=-6p^{2}(3p^4-2q)^2\)
11. \(-32y^{14}+98y^{2}=-2y^{2}(16y^{12}-49)=-2y^{2}(4y^6+7)(4y^6-7)\)
12. \(-16p^{21}+25p^{5}=-p^{5}(16p^{16}-25)=-p^{5}(4p^8+5)(4p^8-5)\)