Ontbinden in factoren (2)

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

1. \(-108s^{5}+180s^{4}-75s^{3}\)
2. \(72a^{7}-50a^{5}\)
3. \(-384s^{4}-672s^{3}-294s^{2}\)
4. \(-50p^{7}+80p^{6}-32p^{5}\)
5. \(-75q^{17}+108q^{5}\)
6. \(-80a^{5}+280a^{4}-245a^{3}\)
7. \(125s^{7}+400s^{6}+320s^{5}\)
8. \(-8y^{6}+18y^{4}\)
9. \(-49a^{12}-42a^{8}q-9a^{4}q^2\)
10. \(320s^{13}+400s^{9}+125s^{5}\)
11. \(-6p^{6}+150p^{4}\)
12. \(75q^{10}-3q^{4}\)

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

Verbetersleutel

1. \(-108s^{5}+180s^{4}-75s^{3}=-3s^{3}(36s^{2}-60s+25)=-3s^{3}(6s-5)^2\)
2. \(72a^{7}-50a^{5}=2a^{5}(36a^{2}-25)=2a^{5}(6a+5)(6a-5)\)
3. \(-384s^{4}-672s^{3}-294s^{2}=-6s^{2}(64s^{2}+112s+49)=-6s^{2}(8s+7)^2\)
4. \(-50p^{7}+80p^{6}-32p^{5}=-2p^{5}(25p^{2}-40p+16)=-2p^{5}(5p-4)^2\)
5. \(-75q^{17}+108q^{5}=-3q^{5}(25q^{12}-36)=-3q^{5}(5q^6+6)(5q^6-6)\)
6. \(-80a^{5}+280a^{4}-245a^{3}=-5a^{3}(16a^{2}-56a+49)=-5a^{3}(4a-7)^2\)
7. \(125s^{7}+400s^{6}+320s^{5}=5s^{5}(25s^{2}+80s+64)=5s^{5}(5s+8)^2\)
8. \(-8y^{6}+18y^{4}=-2y^{4}(4y^{2}-9)=-2y^{4}(2y+3)(2y-3)\)
9. \(-49a^{12}-42a^{8}q-9a^{4}q^2=-a^{4}(49a^{8}+42a^4q+9q^2)=-a^{4}(7a^4+3q)^2\)
10. \(320s^{13}+400s^{9}+125s^{5}=5s^{5}(64s^{8}+80s^4+25)=5s^{5}(8s^4+5)^2\)
11. \(-6p^{6}+150p^{4}=-6p^{4}(p^2-25)=-6p^{4}(p-5)(p+5)\)
12. \(75q^{10}-3q^{4}=3q^{4}(25q^{6}-1)=3q^{4}(5q^3+1)(5q^3-1)\)