Ontbinden in factoren (2)

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

1. \(x^{5}-18x^{4}+81x^{3}\)
2. \(192a^{4}-240a^{3}+75a^{2}\)
3. \(-5y^{4}+30y^{3}-45y^{2}\)
4. \(-5q^{7}+20q^{5}\)
5. \(-5p^{5}-50p^{4}-125p^{3}\)
6. \(-108s^{6}-180s^{4}-75s^{2}\)
7. \(-245b^{6}+140b^{4}-20b^{2}\)
8. \(-8a^{7}+2a^{5}\)
9. \(125s^{12}-200s^{8}+80s^{4}\)
10. \(-6y^{6}-24y^{5}-24y^{4}\)
11. \(24x^{7}+72x^{6}+54x^{5}\)
12. \(-6s^{6}-72s^{5}-216s^{4}\)

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

Verbetersleutel

1. \(x^{5}-18x^{4}+81x^{3}=x^{3}(x^2-18x+81)=x^{3}(x-9)^2\)
2. \(192a^{4}-240a^{3}+75a^{2}=3a^{2}(64a^{2}-80a+25)=3a^{2}(8a-5)^2\)
3. \(-5y^{4}+30y^{3}-45y^{2}=-5y^{2}(y^2-6y+9)=-5y^{2}(y-3)^2\)
4. \(-5q^{7}+20q^{5}=-5q^{5}(q^2-4)=-5q^{5}(q-2)(q+2)\)
5. \(-5p^{5}-50p^{4}-125p^{3}=-5p^{3}(p^2+10p+25)=-5p^{3}(p+5)^2\)
6. \(-108s^{6}-180s^{4}-75s^{2}=-3s^{2}(36s^{4}+60s^2+25)=-3s^{2}(6s^2+5)^2\)
7. \(-245b^{6}+140b^{4}-20b^{2}=-5b^{2}(49b^{4}-28b^2+4)=-5b^{2}(7b^2-2)^2\)
8. \(-8a^{7}+2a^{5}=-2a^{5}(4a^{2}-1)=-2a^{5}(2a+1)(2a-1)\)
9. \(125s^{12}-200s^{8}+80s^{4}=5s^{4}(25s^{8}-40s^4+16)=5s^{4}(5s^4-4)^2\)
10. \(-6y^{6}-24y^{5}-24y^{4}=-6y^{4}(y^2+4y+4)=-6y^{4}(y+2)^2\)
11. \(24x^{7}+72x^{6}+54x^{5}=6x^{5}(4x^{2}+12x+9)=6x^{5}(2x+3)^2\)
12. \(-6s^{6}-72s^{5}-216s^{4}=-6s^{4}(s^2+12s+36)=-6s^{4}(s+6)^2\)