Ontbinden in factoren (2)

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

1. \(-192a^{9}-240a^{6}-75a^{3}\)
2. \(5x^{6}-10x^{5}+5x^{4}\)
3. \(75q^{4}+60q^{3}+12q^{2}\)
4. \(-6q^{5}+48q^{4}-96q^{3}\)
5. \(-384b^{6}-96b^{4}-6b^{2}\)
6. \(3a^{4}-192a^{2}\)
7. \(-25q^{5}-80q^{4}-64q^{3}\)
8. \(180p^{15}-300p^{10}+125p^{5}\)
9. \(-5p^{4}+90p^{3}-405p^{2}\)
10. \(-96q^{6}+6q^{4}\)
11. \(8s^{8}+8s^{5}x+2s^{2}x^2\)
12. \(-32a^{6}+112a^{5}-98a^{4}\)

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

Verbetersleutel

1. \(-192a^{9}-240a^{6}-75a^{3}=-3a^{3}(64a^{6}+80a^3+25)=-3a^{3}(8a^3+5)^2\)
2. \(5x^{6}-10x^{5}+5x^{4}=5x^{4}(x^2-2x+1)=5x^{4}(x-1)^2\)
3. \(75q^{4}+60q^{3}+12q^{2}=3q^{2}(25q^{2}+20q+4)=3q^{2}(5q+2)^2\)
4. \(-6q^{5}+48q^{4}-96q^{3}=-6q^{3}(q^2-8q+16)=-6q^{3}(q-4)^2\)
5. \(-384b^{6}-96b^{4}-6b^{2}=-6b^{2}(64b^{4}+16b^2+1)=-6b^{2}(8b^2+1)^2\)
6. \(3a^{4}-192a^{2}=3a^{2}(a^2-64)=3a^{2}(a-8)(a+8)\)
7. \(-25q^{5}-80q^{4}-64q^{3}=-q^{3}(25q^{2}+80q+64)=-q^{3}(5q+8)^2\)
8. \(180p^{15}-300p^{10}+125p^{5}=5p^{5}(36p^{10}-60p^5+25)=5p^{5}(6p^5-5)^2\)
9. \(-5p^{4}+90p^{3}-405p^{2}=-5p^{2}(p^2-18p+81)=-5p^{2}(p-9)^2\)
10. \(-96q^{6}+6q^{4}=-6q^{4}(16q^{2}-1)=-6q^{4}(4q+1)(4q-1)\)
11. \(8s^{8}+8s^{5}x+2s^{2}x^2=2s^{2}(4s^{6}+4s^3x+x^2)=2s^{2}(2s^3+x)^2\)
12. \(-32a^{6}+112a^{5}-98a^{4}=-2a^{4}(16a^{2}-56a+49)=-2a^{4}(4a-7)^2\)