Ontbinden in factoren (2)

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

1. \(-12b^{6}+3b^{4}\)
2. \(-36b^{14}-60b^{9}y-25b^{4}y^2\)
3. \(-4p^{7}+9p^{5}\)
4. \(-18q^{5}+96q^{4}-128q^{3}\)
5. \(-54a^{7}-180a^{5}q-150a^{3}q^2\)
6. \(98q^{5}+224q^{4}+128q^{3}\)
7. \(36q^{12}-q^{2}\)
8. \(-27p^{16}+12p^{4}\)
9. \(-3b^{6}+192b^{4}\)
10. \(-147s^{7}+378s^{6}-243s^{5}\)
11. \(6x^{7}+60x^{6}+150x^{5}\)
12. \(-50p^{19}+2p^{5}\)

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

Verbetersleutel

1. \(-12b^{6}+3b^{4}=-3b^{4}(4b^{2}-1)=-3b^{4}(2b+1)(2b-1)\)
2. \(-36b^{14}-60b^{9}y-25b^{4}y^2=-b^{4}(36b^{10}+60b^5y+25y^2)=-b^{4}(6b^5+5y)^2\)
3. \(-4p^{7}+9p^{5}=-p^{5}(4p^{2}-9)=-p^{5}(2p+3)(2p-3)\)
4. \(-18q^{5}+96q^{4}-128q^{3}=-2q^{3}(9q^{2}-48q+64)=-2q^{3}(3q-8)^2\)
5. \(-54a^{7}-180a^{5}q-150a^{3}q^2=-6a^{3}(9a^{4}+30a^2q+25q^2)=-6a^{3}(3a^2+5q)^2\)
6. \(98q^{5}+224q^{4}+128q^{3}=2q^{3}(49q^{2}+112q+64)=2q^{3}(7q+8)^2\)
7. \(36q^{12}-q^{2}=q^{2}(36q^{10}-1)=q^{2}(6q^5+1)(6q^5-1)\)
8. \(-27p^{16}+12p^{4}=-3p^{4}(9p^{12}-4)=-3p^{4}(3p^6+2)(3p^6-2)\)
9. \(-3b^{6}+192b^{4}=-3b^{4}(b^2-64)=-3b^{4}(b-8)(b+8)\)
10. \(-147s^{7}+378s^{6}-243s^{5}=-3s^{5}(49s^{2}-126s+81)=-3s^{5}(7s-9)^2\)
11. \(6x^{7}+60x^{6}+150x^{5}=6x^{5}(x^2+10x+25)=6x^{5}(x+5)^2\)
12. \(-50p^{19}+2p^{5}=-2p^{5}(25p^{14}-1)=-2p^{5}(5p^7+1)(5p^7-1)\)