Ontbinden in factoren (2)

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

1. \(98p^{9}-168p^{7}q+72p^{5}q^2\)
2. \(-12x^{14}-12x^{9}-3x^{4}\)
3. \(72b^{7}+24b^{6}+2b^{5}\)
4. \(-216y^{11}+360y^{8}-150y^{5}\)
5. \(-24b^{10}-24b^{7}p-6b^{4}p^2\)
6. \(50q^{13}-80q^{8}s+32q^{3}s^2\)
7. \(-16p^{8}+56p^{6}-49p^{4}\)
8. \(32b^{7}+80b^{5}s+50b^{3}s^2\)
9. \(-64p^{9}+80p^{7}-25p^{5}\)
10. \(54q^{4}-294q^{2}\)
11. \(-3x^{6}-12x^{5}-12x^{4}\)
12. \(-6b^{7}-108b^{6}-486b^{5}\)

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

Verbetersleutel

1. \(98p^{9}-168p^{7}q+72p^{5}q^2=2p^{5}(49p^{4}-84p^2q+36q^2)=2p^{5}(7p^2-6q)^2\)
2. \(-12x^{14}-12x^{9}-3x^{4}=-3x^{4}(4x^{10}+4x^5+1)=-3x^{4}(2x^5+1)^2\)
3. \(72b^{7}+24b^{6}+2b^{5}=2b^{5}(36b^{2}+12b+1)=2b^{5}(6b+1)^2\)
4. \(-216y^{11}+360y^{8}-150y^{5}=-6y^{5}(36y^{6}-60y^3+25)=-6y^{5}(6y^3-5)^2\)
5. \(-24b^{10}-24b^{7}p-6b^{4}p^2=-6b^{4}(4b^{6}+4b^3p+p^2)=-6b^{4}(2b^3+p)^2\)
6. \(50q^{13}-80q^{8}s+32q^{3}s^2=2q^{3}(25q^{10}-40q^5s+16s^2)=2q^{3}(5q^5-4s)^2\)
7. \(-16p^{8}+56p^{6}-49p^{4}=-p^{4}(16p^{4}-56p^2+49)=-p^{4}(4p^2-7)^2\)
8. \(32b^{7}+80b^{5}s+50b^{3}s^2=2b^{3}(16b^{4}+40b^2s+25s^2)=2b^{3}(4b^2+5s)^2\)
9. \(-64p^{9}+80p^{7}-25p^{5}=-p^{5}(64p^{4}-80p^2+25)=-p^{5}(8p^2-5)^2\)
10. \(54q^{4}-294q^{2}=6q^{2}(9q^{2}-49)=6q^{2}(3q+7)(3q-7)\)
11. \(-3x^{6}-12x^{5}-12x^{4}=-3x^{4}(x^2+4x+4)=-3x^{4}(x+2)^2\)
12. \(-6b^{7}-108b^{6}-486b^{5}=-6b^{5}(b^2+18b+81)=-6b^{5}(b+9)^2\)