Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(-5p^{5}+125p^{3}\)
2. \(-147b^{11}+252b^{7}p-108b^{3}p^2\)
3. \(3x^{5}-36x^{4}+108x^{3}\)
4. \(-96x^{6}+6x^{4}\)
5. \(50s^{16}-72s^{4}\)
6. \(-125a^{19}+45a^{5}\)
7. \(6y^{6}-96y^{4}\)
8. \(-5p^{5}+30p^{4}-45p^{3}\)
9. \(24p^{13}+24p^{9}+6p^{5}\)
10. \(-6x^{5}+6x^{3}\)
11. \(9b^{10}+12b^{7}p+4b^{4}p^2\)
12. \(-5s^{6}+20s^{5}-20s^{4}\)

---

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

Verbetersleutel

1. \(-5p^{5}+125p^{3}=-5p^{3}(p^2-25)=-5p^{3}(p-5)(p+5)\)
2. \(-147b^{11}+252b^{7}p-108b^{3}p^2=-3b^{3}(49b^{8}-84b^4p+36p^2)=-3b^{3}(7b^4-6p)^2\)
3. \(3x^{5}-36x^{4}+108x^{3}=3x^{3}(x^2-12x+36)=3x^{3}(x-6)^2\)
4. \(-96x^{6}+6x^{4}=-6x^{4}(16x^{2}-1)=-6x^{4}(4x+1)(4x-1)\)
5. \(50s^{16}-72s^{4}=2s^{4}(25s^{12}-36)=2s^{4}(5s^6+6)(5s^6-6)\)
6. \(-125a^{19}+45a^{5}=-5a^{5}(25a^{14}-9)=-5a^{5}(5a^7+3)(5a^7-3)\)
7. \(6y^{6}-96y^{4}=6y^{4}(y^2-16)=6y^{4}(y+4)(y-4)\)
8. \(-5p^{5}+30p^{4}-45p^{3}=-5p^{3}(p^2-6p+9)=-5p^{3}(p-3)^2\)
9. \(24p^{13}+24p^{9}+6p^{5}=6p^{5}(4p^{8}+4p^4+1)=6p^{5}(2p^4+1)^2\)
10. \(-6x^{5}+6x^{3}=-6x^{3}(x^2-1)=-6x^{3}(x+1)(x-1)\)
11. \(9b^{10}+12b^{7}p+4b^{4}p^2=b^{4}(9b^{6}+12b^3p+4p^2)=b^{4}(3b^3+2p)^2\)
12. \(-5s^{6}+20s^{5}-20s^{4}=-5s^{4}(s^2-4s+4)=-5s^{4}(s-2)^2\)