Ontbinden in factoren (2)

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

1. \(-9a^{11}+12a^{8}q-4a^{5}q^2\)
2. \(-5x^{6}+70x^{5}-245x^{4}\)
3. \(3a^{7}-27a^{5}\)
4. \(-125p^{7}+320p^{5}\)
5. \(3p^{7}-147p^{5}\)
6. \(-3y^{4}+75y^{2}\)
7. \(80y^{21}-125y^{5}\)
8. \(36q^{7}+84q^{5}+49q^{3}\)
9. \(-245b^{4}-630b^{3}-405b^{2}\)
10. \(125s^{13}-180s^{5}\)
11. \(180q^{7}-5q^{5}\)
12. \(36q^{7}-60q^{6}+25q^{5}\)

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

Verbetersleutel

1. \(-9a^{11}+12a^{8}q-4a^{5}q^2=-a^{5}(9a^{6}-12a^3q+4q^2)=-a^{5}(3a^3-2q)^2\)
2. \(-5x^{6}+70x^{5}-245x^{4}=-5x^{4}(x^2-14x+49)=-5x^{4}(x-7)^2\)
3. \(3a^{7}-27a^{5}=3a^{5}(a^2-9)=3a^{5}(a-3)(a+3)\)
4. \(-125p^{7}+320p^{5}=-5p^{5}(25p^{2}-64)=-5p^{5}(5p+8)(5p-8)\)
5. \(3p^{7}-147p^{5}=3p^{5}(p^2-49)=3p^{5}(p+7)(p-7)\)
6. \(-3y^{4}+75y^{2}=-3y^{2}(y^2-25)=-3y^{2}(y+5)(y-5)\)
7. \(80y^{21}-125y^{5}=5y^{5}(16y^{16}-25)=5y^{5}(4y^8+5)(4y^8-5)\)
8. \(36q^{7}+84q^{5}+49q^{3}=q^{3}(36q^{4}+84q^2+49)=q^{3}(6q^2+7)^2\)
9. \(-245b^{4}-630b^{3}-405b^{2}=-5b^{2}(49b^{2}+126b+81)=-5b^{2}(7b+9)^2\)
10. \(125s^{13}-180s^{5}=5s^{5}(25s^{8}-36)=5s^{5}(5s^4+6)(5s^4-6)\)
11. \(180q^{7}-5q^{5}=5q^{5}(36q^{2}-1)=5q^{5}(6q+1)(6q-1)\)
12. \(36q^{7}-60q^{6}+25q^{5}=q^{5}(36q^{2}-60q+25)=q^{5}(6q-5)^2\)