Ontbinden in factoren (2)

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

1. \(-180s^{7}-60s^{6}-5s^{5}\)
2. \(-4y^{14}-20y^{9}-25y^{4}\)
3. \(p^{5}-25p^{3}\)
4. \(-150b^{9}-180b^{6}q-54b^{3}q^2\)
5. \(-3s^{7}+27s^{5}\)
6. \(64q^{7}+16q^{6}+q^{5}\)
7. \(-20x^{12}-20x^{8}-5x^{4}\)
8. \(2b^{6}-18b^{4}\)
9. \(96b^{7}-294b^{5}\)
10. \(-192a^{13}+336a^{9}p-147a^{5}p^2\)
11. \(80y^{9}+120y^{6}+45y^{3}\)
12. \(-32b^{5}+2b^{3}\)

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

Verbetersleutel

1. \(-180s^{7}-60s^{6}-5s^{5}=-5s^{5}(36s^{2}+12s+1)=-5s^{5}(6s+1)^2\)
2. \(-4y^{14}-20y^{9}-25y^{4}=-y^{4}(4y^{10}+20y^5+25)=-y^{4}(2y^5+5)^2\)
3. \(p^{5}-25p^{3}=p^{3}(p^2-25)=p^{3}(p-5)(p+5)\)
4. \(-150b^{9}-180b^{6}q-54b^{3}q^2=-6b^{3}(25b^{6}+30b^3q+9q^2)=-6b^{3}(5b^3+3q)^2\)
5. \(-3s^{7}+27s^{5}=-3s^{5}(s^2-9)=-3s^{5}(s+3)(s-3)\)
6. \(64q^{7}+16q^{6}+q^{5}=q^{5}(64q^{2}+16q+1)=q^{5}(8q+1)^2\)
7. \(-20x^{12}-20x^{8}-5x^{4}=-5x^{4}(4x^{8}+4x^4+1)=-5x^{4}(2x^4+1)^2\)
8. \(2b^{6}-18b^{4}=2b^{4}(b^2-9)=2b^{4}(b+3)(b-3)\)
9. \(96b^{7}-294b^{5}=6b^{5}(16b^{2}-49)=6b^{5}(4b+7)(4b-7)\)
10. \(-192a^{13}+336a^{9}p-147a^{5}p^2=-3a^{5}(64a^{8}-112a^4p+49p^2)=-3a^{5}(8a^4-7p)^2\)
11. \(80y^{9}+120y^{6}+45y^{3}=5y^{3}(16y^{6}+24y^3+9)=5y^{3}(4y^3+3)^2\)
12. \(-32b^{5}+2b^{3}=-2b^{3}(16b^{2}-1)=-2b^{3}(4b+1)(4b-1)\)