Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(36p^{9}+60p^{7}+25p^{5}\)
2. \(2y^{5}-20y^{4}+50y^{3}\)
3. \(x^{5}-49x^{3}\)
4. \(-75b^{10}+108b^{4}\)
5. \(-6a^{4}+6a^{2}\)
6. \(-3q^{6}-24q^{5}-48q^{4}\)
7. \(5s^{4}-30s^{3}+45s^{2}\)
8. \(-108q^{11}+75q^{3}\)
9. \(20s^{10}+100s^{6}+125s^{2}\)
10. \(36s^{17}-s^{5}\)
11. \(-6q^{5}+150q^{3}\)
12. \(-6s^{4}-48s^{3}-96s^{2}\)

---

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

Verbetersleutel

1. \(36p^{9}+60p^{7}+25p^{5}=p^{5}(36p^{4}+60p^2+25)=p^{5}(6p^2+5)^2\)
2. \(2y^{5}-20y^{4}+50y^{3}=2y^{3}(y^2-10y+25)=2y^{3}(y-5)^2\)
3. \(x^{5}-49x^{3}=x^{3}(x^2-49)=x^{3}(x+7)(x-7)\)
4. \(-75b^{10}+108b^{4}=-3b^{4}(25b^{6}-36)=-3b^{4}(5b^3+6)(5b^3-6)\)
5. \(-6a^{4}+6a^{2}=-6a^{2}(a^2-1)=-6a^{2}(a-1)(a+1)\)
6. \(-3q^{6}-24q^{5}-48q^{4}=-3q^{4}(q^2+8q+16)=-3q^{4}(q+4)^2\)
7. \(5s^{4}-30s^{3}+45s^{2}=5s^{2}(s^2-6s+9)=5s^{2}(s-3)^2\)
8. \(-108q^{11}+75q^{3}=-3q^{3}(36q^{8}-25)=-3q^{3}(6q^4+5)(6q^4-5)\)
9. \(20s^{10}+100s^{6}+125s^{2}=5s^{2}(4s^{8}+20s^4+25)=5s^{2}(2s^4+5)^2\)
10. \(36s^{17}-s^{5}=s^{5}(36s^{12}-1)=s^{5}(6s^6+1)(6s^6-1)\)
11. \(-6q^{5}+150q^{3}=-6q^{3}(q^2-25)=-6q^{3}(q+5)(q-5)\)
12. \(-6s^{4}-48s^{3}-96s^{2}=-6s^{2}(s^2+8s+16)=-6s^{2}(s+4)^2\)