Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(9x^{13}+6x^{9}+x^{5}\)
2. \(49s^{10}-84s^{7}+36s^{4}\)
3. \(-4p^{7}-4p^{6}-p^{5}\)
4. \(54p^{12}-72p^{8}x+24p^{4}x^2\)
5. \(-384p^{9}+672p^{6}s-294p^{3}s^2\)
6. \(54a^{4}-24a^{2}\)
7. \(2y^{5}-36y^{4}+162y^{3}\)
8. \(2q^{6}-2q^{4}\)
9. \(54q^{5}-180q^{4}+150q^{3}\)
10. \(-2b^{4}+4b^{3}-2b^{2}\)
11. \(p^{5}-14p^{4}+49p^{3}\)
12. \(-5b^{4}+45b^{2}\)

---

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

Verbetersleutel

1. \(9x^{13}+6x^{9}+x^{5}=x^{5}(9x^{8}+6x^4+1)=x^{5}(3x^4+1)^2\)
2. \(49s^{10}-84s^{7}+36s^{4}=s^{4}(49s^{6}-84s^3+36)=s^{4}(7s^3-6)^2\)
3. \(-4p^{7}-4p^{6}-p^{5}=-p^{5}(4p^{2}+4p+1)=-p^{5}(2p+1)^2\)
4. \(54p^{12}-72p^{8}x+24p^{4}x^2=6p^{4}(9p^{8}-12p^4x+4x^2)=6p^{4}(3p^4-2x)^2\)
5. \(-384p^{9}+672p^{6}s-294p^{3}s^2=-6p^{3}(64p^{6}-112p^3s+49s^2)=-6p^{3}(8p^3-7s)^2\)
6. \(54a^{4}-24a^{2}=6a^{2}(9a^{2}-4)=6a^{2}(3a+2)(3a-2)\)
7. \(2y^{5}-36y^{4}+162y^{3}=2y^{3}(y^2-18y+81)=2y^{3}(y-9)^2\)
8. \(2q^{6}-2q^{4}=2q^{4}(q^2-1)=2q^{4}(q-1)(q+1)\)
9. \(54q^{5}-180q^{4}+150q^{3}=6q^{3}(9q^{2}-30q+25)=6q^{3}(3q-5)^2\)
10. \(-2b^{4}+4b^{3}-2b^{2}=-2b^{2}(b^2-2b+1)=-2b^{2}(b-1)^2\)
11. \(p^{5}-14p^{4}+49p^{3}=p^{3}(p^2-14p+49)=p^{3}(p-7)^2\)
12. \(-5b^{4}+45b^{2}=-5b^{2}(b^2-9)=-5b^{2}(b-3)(b+3)\)