Ontbinden in factoren (2)

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

1. \(-80a^{8}+120a^{6}-45a^{4}\)
2. \(125s^{7}-100s^{5}+20s^{3}\)
3. \(-45x^{4}+125x^{2}\)
4. \(3p^{4}-75p^{2}\)
5. \(-3q^{6}+18q^{5}-27q^{4}\)
6. \(36b^{10}-60b^{7}+25b^{4}\)
7. \(2s^{6}-24s^{5}+72s^{4}\)
8. \(-5a^{4}+80a^{3}-320a^{2}\)
9. \(-2b^{7}-32b^{6}-128b^{5}\)
10. \(12a^{19}-3a^{5}\)
11. \(-3b^{5}+192b^{3}\)
12. \(-5x^{7}-50x^{6}-125x^{5}\)

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

Verbetersleutel

1. \(-80a^{8}+120a^{6}-45a^{4}=-5a^{4}(16a^{4}-24a^2+9)=-5a^{4}(4a^2-3)^2\)
2. \(125s^{7}-100s^{5}+20s^{3}=5s^{3}(25s^{4}-20s^2+4)=5s^{3}(5s^2-2)^2\)
3. \(-45x^{4}+125x^{2}=-5x^{2}(9x^{2}-25)=-5x^{2}(3x+5)(3x-5)\)
4. \(3p^{4}-75p^{2}=3p^{2}(p^2-25)=3p^{2}(p+5)(p-5)\)
5. \(-3q^{6}+18q^{5}-27q^{4}=-3q^{4}(q^2-6q+9)=-3q^{4}(q-3)^2\)
6. \(36b^{10}-60b^{7}+25b^{4}=b^{4}(36b^{6}-60b^3+25)=b^{4}(6b^3-5)^2\)
7. \(2s^{6}-24s^{5}+72s^{4}=2s^{4}(s^2-12s+36)=2s^{4}(s-6)^2\)
8. \(-5a^{4}+80a^{3}-320a^{2}=-5a^{2}(a^2-16a+64)=-5a^{2}(a-8)^2\)
9. \(-2b^{7}-32b^{6}-128b^{5}=-2b^{5}(b^2+16b+64)=-2b^{5}(b+8)^2\)
10. \(12a^{19}-3a^{5}=3a^{5}(4a^{14}-1)=3a^{5}(2a^7+1)(2a^7-1)\)
11. \(-3b^{5}+192b^{3}=-3b^{3}(b^2-64)=-3b^{3}(b+8)(b-8)\)
12. \(-5x^{7}-50x^{6}-125x^{5}=-5x^{5}(x^2+10x+25)=-5x^{5}(x+5)^2\)