Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(49x^{11}-42x^{8}+9x^{5}\)
2. \(12y^{4}+12y^{3}+3y^{2}\)
3. \(-54s^{6}-252s^{5}-294s^{4}\)
4. \(-27a^{10}+90a^{6}-75a^{2}\)
5. \(-16b^{5}-40b^{4}-25b^{3}\)
6. \(-20q^{7}-20q^{6}-5q^{5}\)
7. \(-50a^{13}-80a^{8}-32a^{3}\)
8. \(20q^{14}+20q^{9}+5q^{4}\)
9. \(p^{6}-25p^{4}\)
10. \(6y^{5}-48y^{4}+96y^{3}\)
11. \(2p^{6}-128p^{4}\)
12. \(-54x^{4}+96x^{2}\)

---

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

Verbetersleutel

1. \(49x^{11}-42x^{8}+9x^{5}=x^{5}(49x^{6}-42x^3+9)=x^{5}(7x^3-3)^2\)
2. \(12y^{4}+12y^{3}+3y^{2}=3y^{2}(4y^{2}+4y+1)=3y^{2}(2y+1)^2\)
3. \(-54s^{6}-252s^{5}-294s^{4}=-6s^{4}(9s^{2}+42s+49)=-6s^{4}(3s+7)^2\)
4. \(-27a^{10}+90a^{6}-75a^{2}=-3a^{2}(9a^{8}-30a^4+25)=-3a^{2}(3a^4-5)^2\)
5. \(-16b^{5}-40b^{4}-25b^{3}=-b^{3}(16b^{2}+40b+25)=-b^{3}(4b+5)^2\)
6. \(-20q^{7}-20q^{6}-5q^{5}=-5q^{5}(4q^{2}+4q+1)=-5q^{5}(2q+1)^2\)
7. \(-50a^{13}-80a^{8}-32a^{3}=-2a^{3}(25a^{10}+40a^5+16)=-2a^{3}(5a^5+4)^2\)
8. \(20q^{14}+20q^{9}+5q^{4}=5q^{4}(4q^{10}+4q^5+1)=5q^{4}(2q^5+1)^2\)
9. \(p^{6}-25p^{4}=p^{4}(p^2-25)=p^{4}(p+5)(p-5)\)
10. \(6y^{5}-48y^{4}+96y^{3}=6y^{3}(y^2-8y+16)=6y^{3}(y-4)^2\)
11. \(2p^{6}-128p^{4}=2p^{4}(p^2-64)=2p^{4}(p-8)(p+8)\)
12. \(-54x^{4}+96x^{2}=-6x^{2}(9x^{2}-16)=-6x^{2}(3x+4)(3x-4)\)