Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(-48y^{6}-120y^{5}-75y^{4}\)
2. \(18y^{21}-98y^{5}\)
3. \(-25x^{14}+4x^{4}\)
4. \(2p^{7}+16p^{6}+32p^{5}\)
5. \(4a^{5}+12a^{4}+9a^{3}\)
6. \(-2p^{4}+36p^{3}-162p^{2}\)
7. \(-2b^{7}+2b^{5}\)
8. \(-64s^{12}-16s^{7}-s^{2}\)
9. \(-3y^{5}+12y^{3}\)
10. \(2p^{7}+20p^{6}+50p^{5}\)
11. \(-54q^{5}-36q^{4}-6q^{3}\)
12. \(128s^{8}-160s^{5}+50s^{2}\)

---

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

Verbetersleutel

1. \(-48y^{6}-120y^{5}-75y^{4}=-3y^{4}(16y^{2}+40y+25)=-3y^{4}(4y+5)^2\)
2. \(18y^{21}-98y^{5}=2y^{5}(9y^{16}-49)=2y^{5}(3y^8+7)(3y^8-7)\)
3. \(-25x^{14}+4x^{4}=-x^{4}(25x^{10}-4)=-x^{4}(5x^5+2)(5x^5-2)\)
4. \(2p^{7}+16p^{6}+32p^{5}=2p^{5}(p^2+8p+16)=2p^{5}(p+4)^2\)
5. \(4a^{5}+12a^{4}+9a^{3}=a^{3}(4a^{2}+12a+9)=a^{3}(2a+3)^2\)
6. \(-2p^{4}+36p^{3}-162p^{2}=-2p^{2}(p^2-18p+81)=-2p^{2}(p-9)^2\)
7. \(-2b^{7}+2b^{5}=-2b^{5}(b^2-1)=-2b^{5}(b-1)(b+1)\)
8. \(-64s^{12}-16s^{7}-s^{2}=-s^{2}(64s^{10}+16s^5+1)=-s^{2}(8s^5+1)^2\)
9. \(-3y^{5}+12y^{3}=-3y^{3}(y^2-4)=-3y^{3}(y+2)(y-2)\)
10. \(2p^{7}+20p^{6}+50p^{5}=2p^{5}(p^2+10p+25)=2p^{5}(p+5)^2\)
11. \(-54q^{5}-36q^{4}-6q^{3}=-6q^{3}(9q^{2}+6q+1)=-6q^{3}(3q+1)^2\)
12. \(128s^{8}-160s^{5}+50s^{2}=2s^{2}(64s^{6}-80s^3+25)=2s^{2}(8s^3-5)^2\)