Ontbinden in factoren (2)

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

1. \(-150q^{6}+420q^{5}-294q^{4}\)
2. \(p^{7}+8p^{6}+16p^{5}\)
3. \(98a^{9}-84a^{6}y+18a^{3}y^2\)
4. \(-6x^{5}-96x^{4}-384x^{3}\)
5. \(-20a^{16}+5a^{4}\)
6. \(-75a^{5}-240a^{4}-192a^{3}\)
7. \(-216x^{4}+360x^{3}-150x^{2}\)
8. \(150b^{6}+420b^{5}+294b^{4}\)
9. \(180q^{6}+300q^{5}+125q^{4}\)
10. \(-36q^{15}-60q^{10}-25q^{5}\)
11. \(36q^{21}-49q^{5}\)
12. \(36s^{6}+12s^{5}+s^{4}\)

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

Verbetersleutel

1. \(-150q^{6}+420q^{5}-294q^{4}=-6q^{4}(25q^{2}-70q+49)=-6q^{4}(5q-7)^2\)
2. \(p^{7}+8p^{6}+16p^{5}=p^{5}(p^2+8p+16)=p^{5}(p+4)^2\)
3. \(98a^{9}-84a^{6}y+18a^{3}y^2=2a^{3}(49a^{6}-42a^3y+9y^2)=2a^{3}(7a^3-3y)^2\)
4. \(-6x^{5}-96x^{4}-384x^{3}=-6x^{3}(x^2+16x+64)=-6x^{3}(x+8)^2\)
5. \(-20a^{16}+5a^{4}=-5a^{4}(4a^{12}-1)=-5a^{4}(2a^6+1)(2a^6-1)\)
6. \(-75a^{5}-240a^{4}-192a^{3}=-3a^{3}(25a^{2}+80a+64)=-3a^{3}(5a+8)^2\)
7. \(-216x^{4}+360x^{3}-150x^{2}=-6x^{2}(36x^{2}-60x+25)=-6x^{2}(6x-5)^2\)
8. \(150b^{6}+420b^{5}+294b^{4}=6b^{4}(25b^{2}+70b+49)=6b^{4}(5b+7)^2\)
9. \(180q^{6}+300q^{5}+125q^{4}=5q^{4}(36q^{2}+60q+25)=5q^{4}(6q+5)^2\)
10. \(-36q^{15}-60q^{10}-25q^{5}=-q^{5}(36q^{10}+60q^5+25)=-q^{5}(6q^5+5)^2\)
11. \(36q^{21}-49q^{5}=q^{5}(36q^{16}-49)=q^{5}(6q^8+7)(6q^8-7)\)
12. \(36s^{6}+12s^{5}+s^{4}=s^{4}(36s^{2}+12s+1)=s^{4}(6s+1)^2\)