Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(-18a^{13}-48a^{8}x-32a^{3}x^2\)
2. \(-5q^{5}+90q^{4}-405q^{3}\)
3. \(4s^{9}+20s^{6}y+25s^{3}y^2\)
4. \(-50p^{7}+2p^{5}\)
5. \(36p^{16}-p^{4}\)
6. \(-5x^{6}+320x^{4}\)
7. \(-128s^{13}-32s^{8}-2s^{3}\)
8. \(108q^{11}+180q^{7}+75q^{3}\)
9. \(-320p^{12}-80p^{7}s-5p^{2}s^2\)
10. \(-5y^{7}-40y^{6}-80y^{5}\)
11. \(2x^{5}-8x^{4}+8x^{3}\)
12. \(-5x^{7}+80x^{6}-320x^{5}\)

---

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

Verbetersleutel

1. \(-18a^{13}-48a^{8}x-32a^{3}x^2=-2a^{3}(9a^{10}+24a^5x+16x^2)=-2a^{3}(3a^5+4x)^2\)
2. \(-5q^{5}+90q^{4}-405q^{3}=-5q^{3}(q^2-18q+81)=-5q^{3}(q-9)^2\)
3. \(4s^{9}+20s^{6}y+25s^{3}y^2=s^{3}(4s^{6}+20s^3y+25y^2)=s^{3}(2s^3+5y)^2\)
4. \(-50p^{7}+2p^{5}=-2p^{5}(25p^{2}-1)=-2p^{5}(5p+1)(5p-1)\)
5. \(36p^{16}-p^{4}=p^{4}(36p^{12}-1)=p^{4}(6p^6+1)(6p^6-1)\)
6. \(-5x^{6}+320x^{4}=-5x^{4}(x^2-64)=-5x^{4}(x+8)(x-8)\)
7. \(-128s^{13}-32s^{8}-2s^{3}=-2s^{3}(64s^{10}+16s^5+1)=-2s^{3}(8s^5+1)^2\)
8. \(108q^{11}+180q^{7}+75q^{3}=3q^{3}(36q^{8}+60q^4+25)=3q^{3}(6q^4+5)^2\)
9. \(-320p^{12}-80p^{7}s-5p^{2}s^2=-5p^{2}(64p^{10}+16p^5s+s^2)=-5p^{2}(8p^5+s)^2\)
10. \(-5y^{7}-40y^{6}-80y^{5}=-5y^{5}(y^2+8y+16)=-5y^{5}(y+4)^2\)
11. \(2x^{5}-8x^{4}+8x^{3}=2x^{3}(x^2-4x+4)=2x^{3}(x-2)^2\)
12. \(-5x^{7}+80x^{6}-320x^{5}=-5x^{5}(x^2-16x+64)=-5x^{5}(x-8)^2\)