Ontbinden in factoren (2)

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

1. \(-6x^{4}+150x^{2}\)
2. \(245s^{11}+350s^{7}+125s^{3}\)
3. \(-54x^{4}-72x^{3}-24x^{2}\)
4. \(-6b^{5}+384b^{3}\)
5. \(-27x^{7}+48x^{5}\)
6. \(6p^{7}-54p^{5}\)
7. \(a^{4}-2a^{3}+a^{2}\)
8. \(-108x^{13}-180x^{9}y-75x^{5}y^2\)
9. \(-3a^{6}-54a^{5}-243a^{4}\)
10. \(-5s^{6}+60s^{5}-180s^{4}\)
11. \(24a^{12}+24a^{7}+6a^{2}\)
12. \(-108a^{8}+147a^{2}\)

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

Verbetersleutel

1. \(-6x^{4}+150x^{2}=-6x^{2}(x^2-25)=-6x^{2}(x+5)(x-5)\)
2. \(245s^{11}+350s^{7}+125s^{3}=5s^{3}(49s^{8}+70s^4+25)=5s^{3}(7s^4+5)^2\)
3. \(-54x^{4}-72x^{3}-24x^{2}=-6x^{2}(9x^{2}+12x+4)=-6x^{2}(3x+2)^2\)
4. \(-6b^{5}+384b^{3}=-6b^{3}(b^2-64)=-6b^{3}(b-8)(b+8)\)
5. \(-27x^{7}+48x^{5}=-3x^{5}(9x^{2}-16)=-3x^{5}(3x+4)(3x-4)\)
6. \(6p^{7}-54p^{5}=6p^{5}(p^2-9)=6p^{5}(p+3)(p-3)\)
7. \(a^{4}-2a^{3}+a^{2}=a^{2}(a^2-2a+1)=a^{2}(a-1)^2\)
8. \(-108x^{13}-180x^{9}y-75x^{5}y^2=-3x^{5}(36x^{8}+60x^4y+25y^2)=-3x^{5}(6x^4+5y)^2\)
9. \(-3a^{6}-54a^{5}-243a^{4}=-3a^{4}(a^2+18a+81)=-3a^{4}(a+9)^2\)
10. \(-5s^{6}+60s^{5}-180s^{4}=-5s^{4}(s^2-12s+36)=-5s^{4}(s-6)^2\)
11. \(24a^{12}+24a^{7}+6a^{2}=6a^{2}(4a^{10}+4a^5+1)=6a^{2}(2a^5+1)^2\)
12. \(-108a^{8}+147a^{2}=-3a^{2}(36a^{6}-49)=-3a^{2}(6a^3+7)(6a^3-7)\)