Ontbinden in factoren (2)

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

1. \(-8q^{5}-8q^{4}-2q^{3}\)
2. \(24s^{4}+24s^{3}+6s^{2}\)
3. \(-4x^{4}-4x^{3}-x^{2}\)
4. \(-64y^{5}-16y^{4}-y^{3}\)
5. \(6x^{5}-216x^{3}\)
6. \(16b^{6}-25b^{4}\)
7. \(-50y^{7}+180y^{6}-162y^{5}\)
8. \(-5q^{6}+180q^{4}\)
9. \(12a^{9}+12a^{7}x+3a^{5}x^2\)
10. \(-80p^{11}-40p^{8}x-5p^{5}x^2\)
11. \(12a^{7}+60a^{5}s+75a^{3}s^2\)
12. \(-12q^{5}-12q^{4}-3q^{3}\)

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

Verbetersleutel

1. \(-8q^{5}-8q^{4}-2q^{3}=-2q^{3}(4q^{2}+4q+1)=-2q^{3}(2q+1)^2\)
2. \(24s^{4}+24s^{3}+6s^{2}=6s^{2}(4s^{2}+4s+1)=6s^{2}(2s+1)^2\)
3. \(-4x^{4}-4x^{3}-x^{2}=-x^{2}(4x^{2}+4x+1)=-x^{2}(2x+1)^2\)
4. \(-64y^{5}-16y^{4}-y^{3}=-y^{3}(64y^{2}+16y+1)=-y^{3}(8y+1)^2\)
5. \(6x^{5}-216x^{3}=6x^{3}(x^2-36)=6x^{3}(x+6)(x-6)\)
6. \(16b^{6}-25b^{4}=b^{4}(16b^{2}-25)=b^{4}(4b+5)(4b-5)\)
7. \(-50y^{7}+180y^{6}-162y^{5}=-2y^{5}(25y^{2}-90y+81)=-2y^{5}(5y-9)^2\)
8. \(-5q^{6}+180q^{4}=-5q^{4}(q^2-36)=-5q^{4}(q-6)(q+6)\)
9. \(12a^{9}+12a^{7}x+3a^{5}x^2=3a^{5}(4a^{4}+4a^2x+x^2)=3a^{5}(2a^2+x)^2\)
10. \(-80p^{11}-40p^{8}x-5p^{5}x^2=-5p^{5}(16p^{6}+8p^3x+x^2)=-5p^{5}(4p^3+x)^2\)
11. \(12a^{7}+60a^{5}s+75a^{3}s^2=3a^{3}(4a^{4}+20a^2s+25s^2)=3a^{3}(2a^2+5s)^2\)
12. \(-12q^{5}-12q^{4}-3q^{3}=-3q^{3}(4q^{2}+4q+1)=-3q^{3}(2q+1)^2\)