Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(-25s^{7}+s^{5}\)
2. \(-25s^{6}+4s^{4}\)
3. \(-45y^{11}+80y^{5}\)
4. \(-75s^{6}-30s^{5}-3s^{4}\)
5. \(-20s^{4}+245s^{2}\)
6. \(p^{7}-4p^{6}+4p^{5}\)
7. \(-125x^{7}-300x^{6}-180x^{5}\)
8. \(-4p^{5}-4p^{4}-p^{3}\)
9. \(20a^{11}+100a^{8}b+125a^{5}b^2\)
10. \(-27s^{10}+90s^{6}-75s^{2}\)
11. \(320b^{7}+80b^{6}+5b^{5}\)
12. \(18p^{10}+48p^{7}+32p^{4}\)

---

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

Verbetersleutel

1. \(-25s^{7}+s^{5}=-s^{5}(25s^{2}-1)=-s^{5}(5s+1)(5s-1)\)
2. \(-25s^{6}+4s^{4}=-s^{4}(25s^{2}-4)=-s^{4}(5s+2)(5s-2)\)
3. \(-45y^{11}+80y^{5}=-5y^{5}(9y^{6}-16)=-5y^{5}(3y^3+4)(3y^3-4)\)
4. \(-75s^{6}-30s^{5}-3s^{4}=-3s^{4}(25s^{2}+10s+1)=-3s^{4}(5s+1)^2\)
5. \(-20s^{4}+245s^{2}=-5s^{2}(4s^{2}-49)=-5s^{2}(2s+7)(2s-7)\)
6. \(p^{7}-4p^{6}+4p^{5}=p^{5}(p^2-4p+4)=p^{5}(p-2)^2\)
7. \(-125x^{7}-300x^{6}-180x^{5}=-5x^{5}(25x^{2}+60x+36)=-5x^{5}(5x+6)^2\)
8. \(-4p^{5}-4p^{4}-p^{3}=-p^{3}(4p^{2}+4p+1)=-p^{3}(2p+1)^2\)
9. \(20a^{11}+100a^{8}b+125a^{5}b^2=5a^{5}(4a^{6}+20a^3b+25b^2)=5a^{5}(2a^3+5b)^2\)
10. \(-27s^{10}+90s^{6}-75s^{2}=-3s^{2}(9s^{8}-30s^4+25)=-3s^{2}(3s^4-5)^2\)
11. \(320b^{7}+80b^{6}+5b^{5}=5b^{5}(64b^{2}+16b+1)=5b^{5}(8b+1)^2\)
12. \(18p^{10}+48p^{7}+32p^{4}=2p^{4}(9p^{6}+24p^3+16)=2p^{4}(3p^3+4)^2\)