Ontbinden in factoren (2)

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

1. \(-2a^{5}-16a^{4}-32a^{3}\)
2. \(32q^{6}-112q^{5}+98q^{4}\)
3. \(-36p^{13}-60p^{9}x-25p^{5}x^2\)
4. \(180b^{8}+300b^{6}p+125b^{4}p^2\)
5. \(45q^{5}-240q^{4}+320q^{3}\)
6. \(54q^{6}+36q^{4}+6q^{2}\)
7. \(-108p^{6}+75p^{4}\)
8. \(108a^{19}-147a^{5}\)
9. \(25x^{6}+80x^{5}+64x^{4}\)
10. \(16b^{4}+24b^{3}+9b^{2}\)
11. \(-384a^{10}-96a^{6}p-6a^{2}p^2\)
12. \(245b^{8}-420b^{5}x+180b^{2}x^2\)

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

Verbetersleutel

1. \(-2a^{5}-16a^{4}-32a^{3}=-2a^{3}(a^2+8a+16)=-2a^{3}(a+4)^2\)
2. \(32q^{6}-112q^{5}+98q^{4}=2q^{4}(16q^{2}-56q+49)=2q^{4}(4q-7)^2\)
3. \(-36p^{13}-60p^{9}x-25p^{5}x^2=-p^{5}(36p^{8}+60p^4x+25x^2)=-p^{5}(6p^4+5x)^2\)
4. \(180b^{8}+300b^{6}p+125b^{4}p^2=5b^{4}(36b^{4}+60b^2p+25p^2)=5b^{4}(6b^2+5p)^2\)
5. \(45q^{5}-240q^{4}+320q^{3}=5q^{3}(9q^{2}-48q+64)=5q^{3}(3q-8)^2\)
6. \(54q^{6}+36q^{4}+6q^{2}=6q^{2}(9q^{4}+6q^2+1)=6q^{2}(3q^2+1)^2\)
7. \(-108p^{6}+75p^{4}=-3p^{4}(36p^{2}-25)=-3p^{4}(6p+5)(6p-5)\)
8. \(108a^{19}-147a^{5}=3a^{5}(36a^{14}-49)=3a^{5}(6a^7+7)(6a^7-7)\)
9. \(25x^{6}+80x^{5}+64x^{4}=x^{4}(25x^{2}+80x+64)=x^{4}(5x+8)^2\)
10. \(16b^{4}+24b^{3}+9b^{2}=b^{2}(16b^{2}+24b+9)=b^{2}(4b+3)^2\)
11. \(-384a^{10}-96a^{6}p-6a^{2}p^2=-6a^{2}(64a^{8}+16a^4p+p^2)=-6a^{2}(8a^4+p)^2\)
12. \(245b^{8}-420b^{5}x+180b^{2}x^2=5b^{2}(49b^{6}-84b^3x+36x^2)=5b^{2}(7b^3-6x)^2\)