Ontbinden in factoren (2)

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

1. \(-a^{4}-16a^{3}-64a^{2}\)
2. \(-2q^{6}-20q^{5}-50q^{4}\)
3. \(-2b^{4}+98b^{2}\)
4. \(6a^{5}-96a^{3}\)
5. \(-147x^{6}-42x^{5}-3x^{4}\)
6. \(-20a^{13}-20a^{8}-5a^{3}\)
7. \(-180y^{5}+125y^{3}\)
8. \(6x^{7}-72x^{6}+216x^{5}\)
9. \(98s^{4}-84s^{3}+18s^{2}\)
10. \(-98a^{7}-28a^{5}x-2a^{3}x^2\)
11. \(-75x^{5}+270x^{4}-243x^{3}\)
12. \(180q^{8}+60q^{5}+5q^{2}\)

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

Verbetersleutel

1. \(-a^{4}-16a^{3}-64a^{2}=-a^{2}(a^2+16a+64)=-a^{2}(a+8)^2\)
2. \(-2q^{6}-20q^{5}-50q^{4}=-2q^{4}(q^2+10q+25)=-2q^{4}(q+5)^2\)
3. \(-2b^{4}+98b^{2}=-2b^{2}(b^2-49)=-2b^{2}(b-7)(b+7)\)
4. \(6a^{5}-96a^{3}=6a^{3}(a^2-16)=6a^{3}(a-4)(a+4)\)
5. \(-147x^{6}-42x^{5}-3x^{4}=-3x^{4}(49x^{2}+14x+1)=-3x^{4}(7x+1)^2\)
6. \(-20a^{13}-20a^{8}-5a^{3}=-5a^{3}(4a^{10}+4a^5+1)=-5a^{3}(2a^5+1)^2\)
7. \(-180y^{5}+125y^{3}=-5y^{3}(36y^{2}-25)=-5y^{3}(6y+5)(6y-5)\)
8. \(6x^{7}-72x^{6}+216x^{5}=6x^{5}(x^2-12x+36)=6x^{5}(x-6)^2\)
9. \(98s^{4}-84s^{3}+18s^{2}=2s^{2}(49s^{2}-42s+9)=2s^{2}(7s-3)^2\)
10. \(-98a^{7}-28a^{5}x-2a^{3}x^2=-2a^{3}(49a^{4}+14a^2x+x^2)=-2a^{3}(7a^2+x)^2\)
11. \(-75x^{5}+270x^{4}-243x^{3}=-3x^{3}(25x^{2}-90x+81)=-3x^{3}(5x-9)^2\)
12. \(180q^{8}+60q^{5}+5q^{2}=5q^{2}(36q^{6}+12q^3+1)=5q^{2}(6q^3+1)^2\)