Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(p^{5}-25p^{3}\)
2. \(216x^{6}-150x^{4}\)
3. \(p^{6}-14p^{5}+49p^{4}\)
4. \(-45s^{4}+5s^{2}\)
5. \(-12x^{4}-84x^{3}-147x^{2}\)
6. \(-4q^{4}+9q^{2}\)
7. \(147b^{7}+126b^{5}q+27b^{3}q^2\)
8. \(45s^{6}+150s^{4}+125s^{2}\)
9. \(27b^{7}-48b^{5}\)
10. \(-80y^{8}+245y^{2}\)
11. \(-36p^{6}-12p^{4}q-p^{2}q^2\)
12. \(-6a^{5}-24a^{4}-24a^{3}\)

---

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

Verbetersleutel

1. \(p^{5}-25p^{3}=p^{3}(p^2-25)=p^{3}(p-5)(p+5)\)
2. \(216x^{6}-150x^{4}=6x^{4}(36x^{2}-25)=6x^{4}(6x+5)(6x-5)\)
3. \(p^{6}-14p^{5}+49p^{4}=p^{4}(p^2-14p+49)=p^{4}(p-7)^2\)
4. \(-45s^{4}+5s^{2}=-5s^{2}(9s^{2}-1)=-5s^{2}(3s+1)(3s-1)\)
5. \(-12x^{4}-84x^{3}-147x^{2}=-3x^{2}(4x^{2}+28x+49)=-3x^{2}(2x+7)^2\)
6. \(-4q^{4}+9q^{2}=-q^{2}(4q^{2}-9)=-q^{2}(2q+3)(2q-3)\)
7. \(147b^{7}+126b^{5}q+27b^{3}q^2=3b^{3}(49b^{4}+42b^2q+9q^2)=3b^{3}(7b^2+3q)^2\)
8. \(45s^{6}+150s^{4}+125s^{2}=5s^{2}(9s^{4}+30s^2+25)=5s^{2}(3s^2+5)^2\)
9. \(27b^{7}-48b^{5}=3b^{5}(9b^{2}-16)=3b^{5}(3b+4)(3b-4)\)
10. \(-80y^{8}+245y^{2}=-5y^{2}(16y^{6}-49)=-5y^{2}(4y^3+7)(4y^3-7)\)
11. \(-36p^{6}-12p^{4}q-p^{2}q^2=-p^{2}(36p^{4}+12p^2q+q^2)=-p^{2}(6p^2+q)^2\)
12. \(-6a^{5}-24a^{4}-24a^{3}=-6a^{3}(a^2+4a+4)=-6a^{3}(a+2)^2\)