Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(-8b^{7}-8b^{5}-2b^{3}\)
2. \(5p^{6}-60p^{5}+180p^{4}\)
3. \(-8a^{11}-24a^{7}s-18a^{3}s^2\)
4. \(-125p^{10}+350p^{6}-245p^{2}\)
5. \(-9y^{6}+y^{4}\)
6. \(384s^{13}+480s^{9}x+150s^{5}x^2\)
7. \(150x^{10}+240x^{7}+96x^{4}\)
8. \(-16x^{13}+25x^{3}\)
9. \(-50x^{4}+8x^{2}\)
10. \(20q^{10}-245q^{2}\)
11. \(-18b^{7}+32b^{5}\)
12. \(-48y^{4}+27y^{2}\)

---

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

Verbetersleutel

1. \(-8b^{7}-8b^{5}-2b^{3}=-2b^{3}(4b^{4}+4b^2+1)=-2b^{3}(2b^2+1)^2\)
2. \(5p^{6}-60p^{5}+180p^{4}=5p^{4}(p^2-12p+36)=5p^{4}(p-6)^2\)
3. \(-8a^{11}-24a^{7}s-18a^{3}s^2=-2a^{3}(4a^{8}+12a^4s+9s^2)=-2a^{3}(2a^4+3s)^2\)
4. \(-125p^{10}+350p^{6}-245p^{2}=-5p^{2}(25p^{8}-70p^4+49)=-5p^{2}(5p^4-7)^2\)
5. \(-9y^{6}+y^{4}=-y^{4}(9y^{2}-1)=-y^{4}(3y+1)(3y-1)\)
6. \(384s^{13}+480s^{9}x+150s^{5}x^2=6s^{5}(64s^{8}+80s^4x+25x^2)=6s^{5}(8s^4+5x)^2\)
7. \(150x^{10}+240x^{7}+96x^{4}=6x^{4}(25x^{6}+40x^3+16)=6x^{4}(5x^3+4)^2\)
8. \(-16x^{13}+25x^{3}=-x^{3}(16x^{10}-25)=-x^{3}(4x^5+5)(4x^5-5)\)
9. \(-50x^{4}+8x^{2}=-2x^{2}(25x^{2}-4)=-2x^{2}(5x+2)(5x-2)\)
10. \(20q^{10}-245q^{2}=5q^{2}(4q^{8}-49)=5q^{2}(2q^4+7)(2q^4-7)\)
11. \(-18b^{7}+32b^{5}=-2b^{5}(9b^{2}-16)=-2b^{5}(3b+4)(3b-4)\)
12. \(-48y^{4}+27y^{2}=-3y^{2}(16y^{2}-9)=-3y^{2}(4y+3)(4y-3)\)