Ontbinden in factoren (2)

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

1. \(-80p^{13}-40p^{8}x-5p^{3}x^2\)
2. \(-2y^{6}+72y^{4}\)
3. \(75y^{10}-3y^{4}\)
4. \(16q^{4}+40q^{3}+25q^{2}\)
5. \(-5a^{4}+320a^{2}\)
6. \(-8q^{11}-8q^{7}-2q^{3}\)
7. \(4y^{14}-25y^{4}\)
8. \(-80q^{13}+120q^{9}s-45q^{5}s^2\)
9. \(-54b^{6}+180b^{4}-150b^{2}\)
10. \(-320a^{7}+560a^{5}b-245a^{3}b^2\)
11. \(-3x^{4}+48x^{2}\)
12. \(-45s^{7}+150s^{6}-125s^{5}\)

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

Verbetersleutel

1. \(-80p^{13}-40p^{8}x-5p^{3}x^2=-5p^{3}(16p^{10}+8p^5x+x^2)=-5p^{3}(4p^5+x)^2\)
2. \(-2y^{6}+72y^{4}=-2y^{4}(y^2-36)=-2y^{4}(y-6)(y+6)\)
3. \(75y^{10}-3y^{4}=3y^{4}(25y^{6}-1)=3y^{4}(5y^3+1)(5y^3-1)\)
4. \(16q^{4}+40q^{3}+25q^{2}=q^{2}(16q^{2}+40q+25)=q^{2}(4q+5)^2\)
5. \(-5a^{4}+320a^{2}=-5a^{2}(a^2-64)=-5a^{2}(a+8)(a-8)\)
6. \(-8q^{11}-8q^{7}-2q^{3}=-2q^{3}(4q^{8}+4q^4+1)=-2q^{3}(2q^4+1)^2\)
7. \(4y^{14}-25y^{4}=y^{4}(4y^{10}-25)=y^{4}(2y^5+5)(2y^5-5)\)
8. \(-80q^{13}+120q^{9}s-45q^{5}s^2=-5q^{5}(16q^{8}-24q^4s+9s^2)=-5q^{5}(4q^4-3s)^2\)
9. \(-54b^{6}+180b^{4}-150b^{2}=-6b^{2}(9b^{4}-30b^2+25)=-6b^{2}(3b^2-5)^2\)
10. \(-320a^{7}+560a^{5}b-245a^{3}b^2=-5a^{3}(64a^{4}-112a^2b+49b^2)=-5a^{3}(8a^2-7b)^2\)
11. \(-3x^{4}+48x^{2}=-3x^{2}(x^2-16)=-3x^{2}(x-4)(x+4)\)
12. \(-45s^{7}+150s^{6}-125s^{5}=-5s^{5}(9s^{2}-30s+25)=-5s^{5}(3s-5)^2\)