Ontbinden in factoren (2)

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

1. \(-50b^{9}-20b^{6}x-2b^{3}x^2\)
2. \(-75q^{7}+108q^{5}\)
3. \(-36x^{8}+60x^{6}-25x^{4}\)
4. \(-320b^{6}+400b^{4}p-125b^{2}p^2\)
5. \(2b^{4}-98b^{2}\)
6. \(-294q^{9}-84q^{7}s-6q^{5}s^2\)
7. \(-98p^{6}+168p^{5}-72p^{4}\)
8. \(6s^{4}-72s^{3}+216s^{2}\)
9. \(-2x^{6}+72x^{4}\)
10. \(8p^{7}+8p^{5}+2p^{3}\)
11. \(45q^{15}+30q^{10}+5q^{5}\)
12. \(-6a^{6}+384a^{4}\)

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

Verbetersleutel

1. \(-50b^{9}-20b^{6}x-2b^{3}x^2=-2b^{3}(25b^{6}+10b^3x+x^2)=-2b^{3}(5b^3+x)^2\)
2. \(-75q^{7}+108q^{5}=-3q^{5}(25q^{2}-36)=-3q^{5}(5q+6)(5q-6)\)
3. \(-36x^{8}+60x^{6}-25x^{4}=-x^{4}(36x^{4}-60x^2+25)=-x^{4}(6x^2-5)^2\)
4. \(-320b^{6}+400b^{4}p-125b^{2}p^2=-5b^{2}(64b^{4}-80b^2p+25p^2)=-5b^{2}(8b^2-5p)^2\)
5. \(2b^{4}-98b^{2}=2b^{2}(b^2-49)=2b^{2}(b-7)(b+7)\)
6. \(-294q^{9}-84q^{7}s-6q^{5}s^2=-6q^{5}(49q^{4}+14q^2s+s^2)=-6q^{5}(7q^2+s)^2\)
7. \(-98p^{6}+168p^{5}-72p^{4}=-2p^{4}(49p^{2}-84p+36)=-2p^{4}(7p-6)^2\)
8. \(6s^{4}-72s^{3}+216s^{2}=6s^{2}(s^2-12s+36)=6s^{2}(s-6)^2\)
9. \(-2x^{6}+72x^{4}=-2x^{4}(x^2-36)=-2x^{4}(x+6)(x-6)\)
10. \(8p^{7}+8p^{5}+2p^{3}=2p^{3}(4p^{4}+4p^2+1)=2p^{3}(2p^2+1)^2\)
11. \(45q^{15}+30q^{10}+5q^{5}=5q^{5}(9q^{10}+6q^5+1)=5q^{5}(3q^5+1)^2\)
12. \(-6a^{6}+384a^{4}=-6a^{4}(a^2-64)=-6a^{4}(a+8)(a-8)\)