Ontbinden in factoren (2)

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

1. \(-147x^{5}+252x^{4}-108x^{3}\)
2. \(-27q^{7}+3q^{5}\)
3. \(-50q^{6}+40q^{5}-8q^{4}\)
4. \(-18b^{10}+60b^{6}p-50b^{2}p^2\)
5. \(54s^{4}-96s^{2}\)
6. \(-27p^{8}-18p^{6}q-3p^{4}q^2\)
7. \(72p^{7}-2p^{5}\)
8. \(-245y^{4}-560y^{3}-320y^{2}\)
9. \(-4x^{7}-4x^{6}-x^{5}\)
10. \(-108b^{7}+180b^{6}-75b^{5}\)
11. \(24b^{4}+24b^{3}+6b^{2}\)
12. \(27x^{10}-3x^{2}\)

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

Verbetersleutel

1. \(-147x^{5}+252x^{4}-108x^{3}=-3x^{3}(49x^{2}-84x+36)=-3x^{3}(7x-6)^2\)
2. \(-27q^{7}+3q^{5}=-3q^{5}(9q^{2}-1)=-3q^{5}(3q+1)(3q-1)\)
3. \(-50q^{6}+40q^{5}-8q^{4}=-2q^{4}(25q^{2}-20q+4)=-2q^{4}(5q-2)^2\)
4. \(-18b^{10}+60b^{6}p-50b^{2}p^2=-2b^{2}(9b^{8}-30b^4p+25p^2)=-2b^{2}(3b^4-5p)^2\)
5. \(54s^{4}-96s^{2}=6s^{2}(9s^{2}-16)=6s^{2}(3s+4)(3s-4)\)
6. \(-27p^{8}-18p^{6}q-3p^{4}q^2=-3p^{4}(9p^{4}+6p^2q+q^2)=-3p^{4}(3p^2+q)^2\)
7. \(72p^{7}-2p^{5}=2p^{5}(36p^{2}-1)=2p^{5}(6p+1)(6p-1)\)
8. \(-245y^{4}-560y^{3}-320y^{2}=-5y^{2}(49y^{2}+112y+64)=-5y^{2}(7y+8)^2\)
9. \(-4x^{7}-4x^{6}-x^{5}=-x^{5}(4x^{2}+4x+1)=-x^{5}(2x+1)^2\)
10. \(-108b^{7}+180b^{6}-75b^{5}=-3b^{5}(36b^{2}-60b+25)=-3b^{5}(6b-5)^2\)
11. \(24b^{4}+24b^{3}+6b^{2}=6b^{2}(4b^{2}+4b+1)=6b^{2}(2b+1)^2\)
12. \(27x^{10}-3x^{2}=3x^{2}(9x^{8}-1)=3x^{2}(3x^4+1)(3x^4-1)\)