Ontbinden in factoren (2)

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

1. \(-6q^{4}-12q^{3}-6q^{2}\)
2. \(-8p^{5}-56p^{4}-98p^{3}\)
3. \(-24b^{10}-120b^{6}q-150b^{2}q^2\)
4. \(-32p^{6}-48p^{4}-18p^{2}\)
5. \(16s^{19}-49s^{3}\)
6. \(54a^{15}+252a^{10}b+294a^{5}b^2\)
7. \(32p^{5}-112p^{4}+98p^{3}\)
8. \(320p^{5}+80p^{4}+5p^{3}\)
9. \(-8p^{4}+98p^{2}\)
10. \(-6b^{6}+384b^{4}\)
11. \(-16q^{9}-40q^{6}x-25q^{3}x^2\)
12. \(-32x^{6}-16x^{5}-2x^{4}\)

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

Verbetersleutel

1. \(-6q^{4}-12q^{3}-6q^{2}=-6q^{2}(q^2+2q+1)=-6q^{2}(q+1)^2\)
2. \(-8p^{5}-56p^{4}-98p^{3}=-2p^{3}(4p^{2}+28p+49)=-2p^{3}(2p+7)^2\)
3. \(-24b^{10}-120b^{6}q-150b^{2}q^2=-6b^{2}(4b^{8}+20b^4q+25q^2)=-6b^{2}(2b^4+5q)^2\)
4. \(-32p^{6}-48p^{4}-18p^{2}=-2p^{2}(16p^{4}+24p^2+9)=-2p^{2}(4p^2+3)^2\)
5. \(16s^{19}-49s^{3}=s^{3}(16s^{16}-49)=s^{3}(4s^8+7)(4s^8-7)\)
6. \(54a^{15}+252a^{10}b+294a^{5}b^2=6a^{5}(9a^{10}+42a^5b+49b^2)=6a^{5}(3a^5+7b)^2\)
7. \(32p^{5}-112p^{4}+98p^{3}=2p^{3}(16p^{2}-56p+49)=2p^{3}(4p-7)^2\)
8. \(320p^{5}+80p^{4}+5p^{3}=5p^{3}(64p^{2}+16p+1)=5p^{3}(8p+1)^2\)
9. \(-8p^{4}+98p^{2}=-2p^{2}(4p^{2}-49)=-2p^{2}(2p+7)(2p-7)\)
10. \(-6b^{6}+384b^{4}=-6b^{4}(b^2-64)=-6b^{4}(b-8)(b+8)\)
11. \(-16q^{9}-40q^{6}x-25q^{3}x^2=-q^{3}(16q^{6}+40q^3x+25x^2)=-q^{3}(4q^3+5x)^2\)
12. \(-32x^{6}-16x^{5}-2x^{4}=-2x^{4}(16x^{2}+8x+1)=-2x^{4}(4x+1)^2\)