Ontbinden in factoren (2)

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

1. \(-80x^{12}+280x^{8}-245x^{4}\)
2. \(-12a^{5}-12a^{4}-3a^{3}\)
3. \(-192q^{9}-48q^{6}-3q^{3}\)
4. \(4x^{10}+20x^{7}+25x^{4}\)
5. \(-12x^{13}-60x^{8}y-75x^{3}y^2\)
6. \(-245p^{10}-70p^{6}y-5p^{2}y^2\)
7. \(-25p^{5}-30p^{4}-9p^{3}\)
8. \(48a^{5}-3a^{3}\)
9. \(3y^{6}+18y^{5}+27y^{4}\)
10. \(48q^{12}-72q^{8}x+27q^{4}x^2\)
11. \(216x^{6}-150x^{4}\)
12. \(49s^{9}-84s^{6}x+36s^{3}x^2\)

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

Verbetersleutel

1. \(-80x^{12}+280x^{8}-245x^{4}=-5x^{4}(16x^{8}-56x^4+49)=-5x^{4}(4x^4-7)^2\)
2. \(-12a^{5}-12a^{4}-3a^{3}=-3a^{3}(4a^{2}+4a+1)=-3a^{3}(2a+1)^2\)
3. \(-192q^{9}-48q^{6}-3q^{3}=-3q^{3}(64q^{6}+16q^3+1)=-3q^{3}(8q^3+1)^2\)
4. \(4x^{10}+20x^{7}+25x^{4}=x^{4}(4x^{6}+20x^3+25)=x^{4}(2x^3+5)^2\)
5. \(-12x^{13}-60x^{8}y-75x^{3}y^2=-3x^{3}(4x^{10}+20x^5y+25y^2)=-3x^{3}(2x^5+5y)^2\)
6. \(-245p^{10}-70p^{6}y-5p^{2}y^2=-5p^{2}(49p^{8}+14p^4y+y^2)=-5p^{2}(7p^4+y)^2\)
7. \(-25p^{5}-30p^{4}-9p^{3}=-p^{3}(25p^{2}+30p+9)=-p^{3}(5p+3)^2\)
8. \(48a^{5}-3a^{3}=3a^{3}(16a^{2}-1)=3a^{3}(4a+1)(4a-1)\)
9. \(3y^{6}+18y^{5}+27y^{4}=3y^{4}(y^2+6y+9)=3y^{4}(y+3)^2\)
10. \(48q^{12}-72q^{8}x+27q^{4}x^2=3q^{4}(16q^{8}-24q^4x+9x^2)=3q^{4}(4q^4-3x)^2\)
11. \(216x^{6}-150x^{4}=6x^{4}(36x^{2}-25)=6x^{4}(6x+5)(6x-5)\)
12. \(49s^{9}-84s^{6}x+36s^{3}x^2=s^{3}(49s^{6}-84s^3x+36x^2)=s^{3}(7s^3-6x)^2\)