Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(6q^{7}+60q^{6}+150q^{5}\)
2. \(-54p^{12}+72p^{7}-24p^{2}\)
3. \(a^{7}-16a^{5}\)
4. \(64b^{6}-112b^{5}+49b^{4}\)
5. \(2p^{6}+8p^{5}+8p^{4}\)
6. \(108x^{5}-147x^{3}\)
7. \(-24a^{11}-24a^{7}p-6a^{3}p^2\)
8. \(36y^{10}-60y^{7}+25y^{4}\)
9. \(-2x^{4}+32x^{2}\)
10. \(25x^{8}+30x^{6}+9x^{4}\)
11. \(-2q^{7}+8q^{5}\)
12. \(25p^{13}-36p^{5}\)

---

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

Verbetersleutel

1. \(6q^{7}+60q^{6}+150q^{5}=6q^{5}(q^2+10q+25)=6q^{5}(q+5)^2\)
2. \(-54p^{12}+72p^{7}-24p^{2}=-6p^{2}(9p^{10}-12p^5+4)=-6p^{2}(3p^5-2)^2\)
3. \(a^{7}-16a^{5}=a^{5}(a^2-16)=a^{5}(a-4)(a+4)\)
4. \(64b^{6}-112b^{5}+49b^{4}=b^{4}(64b^{2}-112b+49)=b^{4}(8b-7)^2\)
5. \(2p^{6}+8p^{5}+8p^{4}=2p^{4}(p^2+4p+4)=2p^{4}(p+2)^2\)
6. \(108x^{5}-147x^{3}=3x^{3}(36x^{2}-49)=3x^{3}(6x+7)(6x-7)\)
7. \(-24a^{11}-24a^{7}p-6a^{3}p^2=-6a^{3}(4a^{8}+4a^4p+p^2)=-6a^{3}(2a^4+p)^2\)
8. \(36y^{10}-60y^{7}+25y^{4}=y^{4}(36y^{6}-60y^3+25)=y^{4}(6y^3-5)^2\)
9. \(-2x^{4}+32x^{2}=-2x^{2}(x^2-16)=-2x^{2}(x+4)(x-4)\)
10. \(25x^{8}+30x^{6}+9x^{4}=x^{4}(25x^{4}+30x^2+9)=x^{4}(5x^2+3)^2\)
11. \(-2q^{7}+8q^{5}=-2q^{5}(q^2-4)=-2q^{5}(q+2)(q-2)\)
12. \(25p^{13}-36p^{5}=p^{5}(25p^{8}-36)=p^{5}(5p^4+6)(5p^4-6)\)