Ontbinden in factoren (2)

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

1. \(-6s^{7}+150s^{5}\)
2. \(54s^{6}-72s^{5}+24s^{4}\)
3. \(-5x^{7}+20x^{5}\)
4. \(s^{4}-16s^{2}\)
5. \(-2q^{5}+2q^{3}\)
6. \(-27b^{14}+90b^{9}y-75b^{4}y^2\)
7. \(150y^{13}-96y^{3}\)
8. \(-4s^{12}-4s^{7}-s^{2}\)
9. \(-245s^{12}+210s^{8}-45s^{4}\)
10. \(-20b^{10}+5b^{2}\)
11. \(180a^{10}+60a^{6}q+5a^{2}q^2\)
12. \(x^{6}-4x^{5}+4x^{4}\)

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

Verbetersleutel

1. \(-6s^{7}+150s^{5}=-6s^{5}(s^2-25)=-6s^{5}(s+5)(s-5)\)
2. \(54s^{6}-72s^{5}+24s^{4}=6s^{4}(9s^{2}-12s+4)=6s^{4}(3s-2)^2\)
3. \(-5x^{7}+20x^{5}=-5x^{5}(x^2-4)=-5x^{5}(x+2)(x-2)\)
4. \(s^{4}-16s^{2}=s^{2}(s^2-16)=s^{2}(s-4)(s+4)\)
5. \(-2q^{5}+2q^{3}=-2q^{3}(q^2-1)=-2q^{3}(q-1)(q+1)\)
6. \(-27b^{14}+90b^{9}y-75b^{4}y^2=-3b^{4}(9b^{10}-30b^5y+25y^2)=-3b^{4}(3b^5-5y)^2\)
7. \(150y^{13}-96y^{3}=6y^{3}(25y^{10}-16)=6y^{3}(5y^5+4)(5y^5-4)\)
8. \(-4s^{12}-4s^{7}-s^{2}=-s^{2}(4s^{10}+4s^5+1)=-s^{2}(2s^5+1)^2\)
9. \(-245s^{12}+210s^{8}-45s^{4}=-5s^{4}(49s^{8}-42s^4+9)=-5s^{4}(7s^4-3)^2\)
10. \(-20b^{10}+5b^{2}=-5b^{2}(4b^{8}-1)=-5b^{2}(2b^4+1)(2b^4-1)\)
11. \(180a^{10}+60a^{6}q+5a^{2}q^2=5a^{2}(36a^{8}+12a^4q+q^2)=5a^{2}(6a^4+q)^2\)
12. \(x^{6}-4x^{5}+4x^{4}=x^{4}(x^2-4x+4)=x^{4}(x-2)^2\)