Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(8s^{11}+40s^{8}+50s^{5}\)
2. \(3y^{6}+18y^{5}+27y^{4}\)
3. \(180y^{10}+60y^{7}+5y^{4}\)
4. \(-96x^{11}+150x^{3}\)
5. \(12p^{11}+12p^{7}x+3p^{3}x^2\)
6. \(-75s^{11}+120s^{8}x-48s^{5}x^2\)
7. \(-27x^{7}+48x^{5}\)
8. \(108b^{4}-3b^{2}\)
9. \(150p^{10}+360p^{7}s+216p^{4}s^2\)
10. \(2x^{4}-28x^{3}+98x^{2}\)
11. \(-5s^{6}-60s^{5}-180s^{4}\)
12. \(-8a^{13}-8a^{8}y-2a^{3}y^2\)

---

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

Verbetersleutel

1. \(8s^{11}+40s^{8}+50s^{5}=2s^{5}(4s^{6}+20s^3+25)=2s^{5}(2s^3+5)^2\)
2. \(3y^{6}+18y^{5}+27y^{4}=3y^{4}(y^2+6y+9)=3y^{4}(y+3)^2\)
3. \(180y^{10}+60y^{7}+5y^{4}=5y^{4}(36y^{6}+12y^3+1)=5y^{4}(6y^3+1)^2\)
4. \(-96x^{11}+150x^{3}=-6x^{3}(16x^{8}-25)=-6x^{3}(4x^4+5)(4x^4-5)\)
5. \(12p^{11}+12p^{7}x+3p^{3}x^2=3p^{3}(4p^{8}+4p^4x+x^2)=3p^{3}(2p^4+x)^2\)
6. \(-75s^{11}+120s^{8}x-48s^{5}x^2=-3s^{5}(25s^{6}-40s^3x+16x^2)=-3s^{5}(5s^3-4x)^2\)
7. \(-27x^{7}+48x^{5}=-3x^{5}(9x^{2}-16)=-3x^{5}(3x+4)(3x-4)\)
8. \(108b^{4}-3b^{2}=3b^{2}(36b^{2}-1)=3b^{2}(6b+1)(6b-1)\)
9. \(150p^{10}+360p^{7}s+216p^{4}s^2=6p^{4}(25p^{6}+60p^3s+36s^2)=6p^{4}(5p^3+6s)^2\)
10. \(2x^{4}-28x^{3}+98x^{2}=2x^{2}(x^2-14x+49)=2x^{2}(x-7)^2\)
11. \(-5s^{6}-60s^{5}-180s^{4}=-5s^{4}(s^2+12s+36)=-5s^{4}(s+6)^2\)
12. \(-8a^{13}-8a^{8}y-2a^{3}y^2=-2a^{3}(4a^{10}+4a^5y+y^2)=-2a^{3}(2a^5+y)^2\)