Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(216s^{5}-6s^{3}\)
2. \(-6q^{6}+84q^{5}-294q^{4}\)
3. \(p^{7}-49p^{5}\)
4. \(-25a^{6}-40a^{5}-16a^{4}\)
5. \(5b^{5}+90b^{4}+405b^{3}\)
6. \(-36s^{11}-60s^{8}y-25s^{5}y^2\)
7. \(-5s^{4}+20s^{2}\)
8. \(72a^{12}+120a^{8}+50a^{4}\)
9. \(-25s^{6}+s^{4}\)
10. \(a^{4}-14a^{3}+49a^{2}\)
11. \(72a^{13}+24a^{9}x+2a^{5}x^2\)
12. \(-54y^{5}+180y^{4}-150y^{3}\)

---

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

Verbetersleutel

1. \(216s^{5}-6s^{3}=6s^{3}(36s^{2}-1)=6s^{3}(6s+1)(6s-1)\)
2. \(-6q^{6}+84q^{5}-294q^{4}=-6q^{4}(q^2-14q+49)=-6q^{4}(q-7)^2\)
3. \(p^{7}-49p^{5}=p^{5}(p^2-49)=p^{5}(p-7)(p+7)\)
4. \(-25a^{6}-40a^{5}-16a^{4}=-a^{4}(25a^{2}+40a+16)=-a^{4}(5a+4)^2\)
5. \(5b^{5}+90b^{4}+405b^{3}=5b^{3}(b^2+18b+81)=5b^{3}(b+9)^2\)
6. \(-36s^{11}-60s^{8}y-25s^{5}y^2=-s^{5}(36s^{6}+60s^3y+25y^2)=-s^{5}(6s^3+5y)^2\)
7. \(-5s^{4}+20s^{2}=-5s^{2}(s^2-4)=-5s^{2}(s+2)(s-2)\)
8. \(72a^{12}+120a^{8}+50a^{4}=2a^{4}(36a^{8}+60a^4+25)=2a^{4}(6a^4+5)^2\)
9. \(-25s^{6}+s^{4}=-s^{4}(25s^{2}-1)=-s^{4}(5s+1)(5s-1)\)
10. \(a^{4}-14a^{3}+49a^{2}=a^{2}(a^2-14a+49)=a^{2}(a-7)^2\)
11. \(72a^{13}+24a^{9}x+2a^{5}x^2=2a^{5}(36a^{8}+12a^4x+x^2)=2a^{5}(6a^4+x)^2\)
12. \(-54y^{5}+180y^{4}-150y^{3}=-6y^{3}(9y^{2}-30y+25)=-6y^{3}(3y-5)^2\)