Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(-p^{4}+49p^{2}\)
2. \(-9q^{11}+16q^{3}\)
3. \(5a^{4}-180a^{2}\)
4. \(12q^{7}+12q^{5}+3q^{3}\)
5. \(-96a^{19}+6a^{5}\)
6. \(150a^{5}-216a^{3}\)
7. \(-216x^{13}-360x^{9}-150x^{5}\)
8. \(-50y^{12}+40y^{8}-8y^{4}\)
9. \(48q^{6}-168q^{5}+147q^{4}\)
10. \(125s^{14}-200s^{9}+80s^{4}\)
11. \(s^{5}+12s^{4}+36s^{3}\)
12. \(125b^{11}-100b^{8}+20b^{5}\)

---

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

Verbetersleutel

1. \(-p^{4}+49p^{2}=-p^{2}(p^2-49)=-p^{2}(p+7)(p-7)\)
2. \(-9q^{11}+16q^{3}=-q^{3}(9q^{8}-16)=-q^{3}(3q^4+4)(3q^4-4)\)
3. \(5a^{4}-180a^{2}=5a^{2}(a^2-36)=5a^{2}(a-6)(a+6)\)
4. \(12q^{7}+12q^{5}+3q^{3}=3q^{3}(4q^{4}+4q^2+1)=3q^{3}(2q^2+1)^2\)
5. \(-96a^{19}+6a^{5}=-6a^{5}(16a^{14}-1)=-6a^{5}(4a^7+1)(4a^7-1)\)
6. \(150a^{5}-216a^{3}=6a^{3}(25a^{2}-36)=6a^{3}(5a+6)(5a-6)\)
7. \(-216x^{13}-360x^{9}-150x^{5}=-6x^{5}(36x^{8}+60x^4+25)=-6x^{5}(6x^4+5)^2\)
8. \(-50y^{12}+40y^{8}-8y^{4}=-2y^{4}(25y^{8}-20y^4+4)=-2y^{4}(5y^4-2)^2\)
9. \(48q^{6}-168q^{5}+147q^{4}=3q^{4}(16q^{2}-56q+49)=3q^{4}(4q-7)^2\)
10. \(125s^{14}-200s^{9}+80s^{4}=5s^{4}(25s^{10}-40s^5+16)=5s^{4}(5s^5-4)^2\)
11. \(s^{5}+12s^{4}+36s^{3}=s^{3}(s^2+12s+36)=s^{3}(s+6)^2\)
12. \(125b^{11}-100b^{8}+20b^{5}=5b^{5}(25b^{6}-20b^3+4)=5b^{5}(5b^3-2)^2\)