Ontbinden in factoren (2)

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

1. \(-125p^{8}+350p^{5}-245p^{2}\)
2. \(-45s^{11}+5s^{5}\)
3. \(-4x^{6}-20x^{5}-25x^{4}\)
4. \(12x^{6}-27x^{4}\)
5. \(-48q^{7}-120q^{6}-75q^{5}\)
6. \(-48q^{7}+27q^{5}\)
7. \(-24q^{8}-120q^{5}-150q^{2}\)
8. \(4a^{9}+4a^{7}b+a^{5}b^2\)
9. \(-b^{6}-18b^{5}-81b^{4}\)
10. \(150x^{4}-240x^{3}+96x^{2}\)
11. \(32a^{12}+80a^{7}+50a^{2}\)
12. \(-6b^{4}+96b^{2}\)

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

Verbetersleutel

1. \(-125p^{8}+350p^{5}-245p^{2}=-5p^{2}(25p^{6}-70p^3+49)=-5p^{2}(5p^3-7)^2\)
2. \(-45s^{11}+5s^{5}=-5s^{5}(9s^{6}-1)=-5s^{5}(3s^3+1)(3s^3-1)\)
3. \(-4x^{6}-20x^{5}-25x^{4}=-x^{4}(4x^{2}+20x+25)=-x^{4}(2x+5)^2\)
4. \(12x^{6}-27x^{4}=3x^{4}(4x^{2}-9)=3x^{4}(2x+3)(2x-3)\)
5. \(-48q^{7}-120q^{6}-75q^{5}=-3q^{5}(16q^{2}+40q+25)=-3q^{5}(4q+5)^2\)
6. \(-48q^{7}+27q^{5}=-3q^{5}(16q^{2}-9)=-3q^{5}(4q+3)(4q-3)\)
7. \(-24q^{8}-120q^{5}-150q^{2}=-6q^{2}(4q^{6}+20q^3+25)=-6q^{2}(2q^3+5)^2\)
8. \(4a^{9}+4a^{7}b+a^{5}b^2=a^{5}(4a^{4}+4a^2b+b^2)=a^{5}(2a^2+b)^2\)
9. \(-b^{6}-18b^{5}-81b^{4}=-b^{4}(b^2+18b+81)=-b^{4}(b+9)^2\)
10. \(150x^{4}-240x^{3}+96x^{2}=6x^{2}(25x^{2}-40x+16)=6x^{2}(5x-4)^2\)
11. \(32a^{12}+80a^{7}+50a^{2}=2a^{2}(16a^{10}+40a^5+25)=2a^{2}(4a^5+5)^2\)
12. \(-6b^{4}+96b^{2}=-6b^{2}(b^2-16)=-6b^{2}(b+4)(b-4)\)