Ontbinden in factoren (2)

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

1. \(-108a^{14}-36a^{9}-3a^{4}\)
2. \(-147x^{6}+252x^{5}-108x^{4}\)
3. \(-72q^{7}-24q^{6}-2q^{5}\)
4. \(-5b^{4}-40b^{3}-80b^{2}\)
5. \(245q^{8}-420q^{6}y+180q^{4}y^2\)
6. \(-3p^{7}+6p^{6}-3p^{5}\)
7. \(-384b^{7}-96b^{5}s-6b^{3}s^2\)
8. \(4q^{5}-9q^{3}\)
9. \(-4p^{6}+49p^{4}\)
10. \(6b^{4}-6b^{2}\)
11. \(96q^{14}-144q^{9}+54q^{4}\)
12. \(-16x^{6}+24x^{5}-9x^{4}\)

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

Verbetersleutel

1. \(-108a^{14}-36a^{9}-3a^{4}=-3a^{4}(36a^{10}+12a^5+1)=-3a^{4}(6a^5+1)^2\)
2. \(-147x^{6}+252x^{5}-108x^{4}=-3x^{4}(49x^{2}-84x+36)=-3x^{4}(7x-6)^2\)
3. \(-72q^{7}-24q^{6}-2q^{5}=-2q^{5}(36q^{2}+12q+1)=-2q^{5}(6q+1)^2\)
4. \(-5b^{4}-40b^{3}-80b^{2}=-5b^{2}(b^2+8b+16)=-5b^{2}(b+4)^2\)
5. \(245q^{8}-420q^{6}y+180q^{4}y^2=5q^{4}(49q^{4}-84q^2y+36y^2)=5q^{4}(7q^2-6y)^2\)
6. \(-3p^{7}+6p^{6}-3p^{5}=-3p^{5}(p^2-2p+1)=-3p^{5}(p-1)^2\)
7. \(-384b^{7}-96b^{5}s-6b^{3}s^2=-6b^{3}(64b^{4}+16b^2s+s^2)=-6b^{3}(8b^2+s)^2\)
8. \(4q^{5}-9q^{3}=q^{3}(4q^{2}-9)=q^{3}(2q+3)(2q-3)\)
9. \(-4p^{6}+49p^{4}=-p^{4}(4p^{2}-49)=-p^{4}(2p+7)(2p-7)\)
10. \(6b^{4}-6b^{2}=6b^{2}(b^2-1)=6b^{2}(b+1)(b-1)\)
11. \(96q^{14}-144q^{9}+54q^{4}=6q^{4}(16q^{10}-24q^5+9)=6q^{4}(4q^5-3)^2\)
12. \(-16x^{6}+24x^{5}-9x^{4}=-x^{4}(16x^{2}-24x+9)=-x^{4}(4x-3)^2\)