Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(3q^{5}+6q^{4}+3q^{3}\)
2. \(-24p^{4}-24p^{3}-6p^{2}\)
3. \(-5s^{5}+20s^{3}\)
4. \(48p^{11}-72p^{8}y+27p^{5}y^2\)
5. \(125b^{13}-180b^{5}\)
6. \(-6s^{7}+36s^{6}-54s^{5}\)
7. \(-24a^{11}-72a^{8}q-54a^{5}q^2\)
8. \(8y^{5}+56y^{4}+98y^{3}\)
9. \(-16p^{6}+9p^{4}\)
10. \(-54a^{8}-36a^{6}-6a^{4}\)
11. \(5s^{5}-80s^{3}\)
12. \(-147b^{9}-42b^{7}-3b^{5}\)

---

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

Verbetersleutel

1. \(3q^{5}+6q^{4}+3q^{3}=3q^{3}(q^2+2q+1)=3q^{3}(q+1)^2\)
2. \(-24p^{4}-24p^{3}-6p^{2}=-6p^{2}(4p^{2}+4p+1)=-6p^{2}(2p+1)^2\)
3. \(-5s^{5}+20s^{3}=-5s^{3}(s^2-4)=-5s^{3}(s+2)(s-2)\)
4. \(48p^{11}-72p^{8}y+27p^{5}y^2=3p^{5}(16p^{6}-24p^3y+9y^2)=3p^{5}(4p^3-3y)^2\)
5. \(125b^{13}-180b^{5}=5b^{5}(25b^{8}-36)=5b^{5}(5b^4+6)(5b^4-6)\)
6. \(-6s^{7}+36s^{6}-54s^{5}=-6s^{5}(s^2-6s+9)=-6s^{5}(s-3)^2\)
7. \(-24a^{11}-72a^{8}q-54a^{5}q^2=-6a^{5}(4a^{6}+12a^3q+9q^2)=-6a^{5}(2a^3+3q)^2\)
8. \(8y^{5}+56y^{4}+98y^{3}=2y^{3}(4y^{2}+28y+49)=2y^{3}(2y+7)^2\)
9. \(-16p^{6}+9p^{4}=-p^{4}(16p^{2}-9)=-p^{4}(4p+3)(4p-3)\)
10. \(-54a^{8}-36a^{6}-6a^{4}=-6a^{4}(9a^{4}+6a^2+1)=-6a^{4}(3a^2+1)^2\)
11. \(5s^{5}-80s^{3}=5s^{3}(s^2-16)=5s^{3}(s+4)(s-4)\)
12. \(-147b^{9}-42b^{7}-3b^{5}=-3b^{5}(49b^{4}+14b^2+1)=-3b^{5}(7b^2+1)^2\)