Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(-128s^{4}-32s^{3}-2s^{2}\)
2. \(6y^{5}+96y^{4}+384y^{3}\)
3. \(-96p^{6}-48p^{5}-6p^{4}\)
4. \(216a^{9}+360a^{6}x+150a^{3}x^2\)
5. \(-5b^{7}+70b^{6}-245b^{5}\)
6. \(20p^{7}-5p^{5}\)
7. \(125x^{9}+200x^{7}+80x^{5}\)
8. \(-54b^{5}-288b^{4}-384b^{3}\)
9. \(-s^{6}+25s^{4}\)
10. \(-216s^{8}-72s^{6}x-6s^{4}x^2\)
11. \(-125a^{4}+180a^{2}\)
12. \(-125b^{5}+245b^{3}\)

---

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

Verbetersleutel

1. \(-128s^{4}-32s^{3}-2s^{2}=-2s^{2}(64s^{2}+16s+1)=-2s^{2}(8s+1)^2\)
2. \(6y^{5}+96y^{4}+384y^{3}=6y^{3}(y^2+16y+64)=6y^{3}(y+8)^2\)
3. \(-96p^{6}-48p^{5}-6p^{4}=-6p^{4}(16p^{2}+8p+1)=-6p^{4}(4p+1)^2\)
4. \(216a^{9}+360a^{6}x+150a^{3}x^2=6a^{3}(36a^{6}+60a^3x+25x^2)=6a^{3}(6a^3+5x)^2\)
5. \(-5b^{7}+70b^{6}-245b^{5}=-5b^{5}(b^2-14b+49)=-5b^{5}(b-7)^2\)
6. \(20p^{7}-5p^{5}=5p^{5}(4p^{2}-1)=5p^{5}(2p+1)(2p-1)\)
7. \(125x^{9}+200x^{7}+80x^{5}=5x^{5}(25x^{4}+40x^2+16)=5x^{5}(5x^2+4)^2\)
8. \(-54b^{5}-288b^{4}-384b^{3}=-6b^{3}(9b^{2}+48b+64)=-6b^{3}(3b+8)^2\)
9. \(-s^{6}+25s^{4}=-s^{4}(s^2-25)=-s^{4}(s-5)(s+5)\)
10. \(-216s^{8}-72s^{6}x-6s^{4}x^2=-6s^{4}(36s^{4}+12s^2x+x^2)=-6s^{4}(6s^2+x)^2\)
11. \(-125a^{4}+180a^{2}=-5a^{2}(25a^{2}-36)=-5a^{2}(5a+6)(5a-6)\)
12. \(-125b^{5}+245b^{3}=-5b^{3}(25b^{2}-49)=-5b^{3}(5b+7)(5b-7)\)