Ontbinden in factoren (2)

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

1. \(-48x^{5}+168x^{4}-147x^{3}\)
2. \(4a^{13}+4a^{8}q+a^{3}q^2\)
3. \(s^{5}-49s^{3}\)
4. \(-2y^{5}+28y^{4}-98y^{3}\)
5. \(-20a^{13}-20a^{8}-5a^{3}\)
6. \(36a^{11}+60a^{8}+25a^{5}\)
7. \(-3q^{4}-42q^{3}-147q^{2}\)
8. \(80b^{6}-5b^{4}\)
9. \(-75s^{4}-120s^{3}-48s^{2}\)
10. \(24s^{6}-294s^{4}\)
11. \(-6p^{4}+294p^{2}\)
12. \(25x^{9}-40x^{6}+16x^{3}\)

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

Verbetersleutel

1. \(-48x^{5}+168x^{4}-147x^{3}=-3x^{3}(16x^{2}-56x+49)=-3x^{3}(4x-7)^2\)
2. \(4a^{13}+4a^{8}q+a^{3}q^2=a^{3}(4a^{10}+4a^5q+q^2)=a^{3}(2a^5+q)^2\)
3. \(s^{5}-49s^{3}=s^{3}(s^2-49)=s^{3}(s-7)(s+7)\)
4. \(-2y^{5}+28y^{4}-98y^{3}=-2y^{3}(y^2-14y+49)=-2y^{3}(y-7)^2\)
5. \(-20a^{13}-20a^{8}-5a^{3}=-5a^{3}(4a^{10}+4a^5+1)=-5a^{3}(2a^5+1)^2\)
6. \(36a^{11}+60a^{8}+25a^{5}=a^{5}(36a^{6}+60a^3+25)=a^{5}(6a^3+5)^2\)
7. \(-3q^{4}-42q^{3}-147q^{2}=-3q^{2}(q^2+14q+49)=-3q^{2}(q+7)^2\)
8. \(80b^{6}-5b^{4}=5b^{4}(16b^{2}-1)=5b^{4}(4b+1)(4b-1)\)
9. \(-75s^{4}-120s^{3}-48s^{2}=-3s^{2}(25s^{2}+40s+16)=-3s^{2}(5s+4)^2\)
10. \(24s^{6}-294s^{4}=6s^{4}(4s^{2}-49)=6s^{4}(2s+7)(2s-7)\)
11. \(-6p^{4}+294p^{2}=-6p^{2}(p^2-49)=-6p^{2}(p+7)(p-7)\)
12. \(25x^{9}-40x^{6}+16x^{3}=x^{3}(25x^{6}-40x^3+16)=x^{3}(5x^3-4)^2\)