Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(-54a^{7}-180a^{6}-150a^{5}\)
2. \(64p^{5}-112p^{4}+49p^{3}\)
3. \(32p^{7}-48p^{5}+18p^{3}\)
4. \(-72y^{6}-120y^{5}-50y^{4}\)
5. \(3b^{6}-3b^{4}\)
6. \(-12q^{6}+27q^{2}\)
7. \(-16s^{9}+56s^{7}x-49s^{5}x^2\)
8. \(3b^{4}-48b^{2}\)
9. \(-6a^{7}+294a^{5}\)
10. \(-49a^{6}+84a^{4}q-36a^{2}q^2\)
11. \(6b^{6}-48b^{5}+96b^{4}\)
12. \(216a^{14}+72a^{9}x+6a^{4}x^2\)

---

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

Verbetersleutel

1. \(-54a^{7}-180a^{6}-150a^{5}=-6a^{5}(9a^{2}+30a+25)=-6a^{5}(3a+5)^2\)
2. \(64p^{5}-112p^{4}+49p^{3}=p^{3}(64p^{2}-112p+49)=p^{3}(8p-7)^2\)
3. \(32p^{7}-48p^{5}+18p^{3}=2p^{3}(16p^{4}-24p^2+9)=2p^{3}(4p^2-3)^2\)
4. \(-72y^{6}-120y^{5}-50y^{4}=-2y^{4}(36y^{2}+60y+25)=-2y^{4}(6y+5)^2\)
5. \(3b^{6}-3b^{4}=3b^{4}(b^2-1)=3b^{4}(b+1)(b-1)\)
6. \(-12q^{6}+27q^{2}=-3q^{2}(4q^{4}-9)=-3q^{2}(2q^2+3)(2q^2-3)\)
7. \(-16s^{9}+56s^{7}x-49s^{5}x^2=-s^{5}(16s^{4}-56s^2x+49x^2)=-s^{5}(4s^2-7x)^2\)
8. \(3b^{4}-48b^{2}=3b^{2}(b^2-16)=3b^{2}(b+4)(b-4)\)
9. \(-6a^{7}+294a^{5}=-6a^{5}(a^2-49)=-6a^{5}(a+7)(a-7)\)
10. \(-49a^{6}+84a^{4}q-36a^{2}q^2=-a^{2}(49a^{4}-84a^2q+36q^2)=-a^{2}(7a^2-6q)^2\)
11. \(6b^{6}-48b^{5}+96b^{4}=6b^{4}(b^2-8b+16)=6b^{4}(b-4)^2\)
12. \(216a^{14}+72a^{9}x+6a^{4}x^2=6a^{4}(36a^{10}+12a^5x+x^2)=6a^{4}(6a^5+x)^2\)