Ontbinden in factoren (2)

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

1. \(96x^{5}-144x^{4}+54x^{3}\)
2. \(5s^{5}-70s^{4}+245s^{3}\)
3. \(12b^{20}-75b^{4}\)
4. \(-72b^{4}-168b^{3}-98b^{2}\)
5. \(80x^{14}+40x^{9}+5x^{4}\)
6. \(-27q^{8}-36q^{5}-12q^{2}\)
7. \(-16a^{6}+56a^{5}-49a^{4}\)
8. \(2q^{4}+36q^{3}+162q^{2}\)
9. \(2x^{6}-8x^{4}\)
10. \(-2a^{6}+8a^{4}\)
11. \(80a^{11}-120a^{7}p+45a^{3}p^2\)
12. \(-2s^{5}+28s^{4}-98s^{3}\)

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

Verbetersleutel

1. \(96x^{5}-144x^{4}+54x^{3}=6x^{3}(16x^{2}-24x+9)=6x^{3}(4x-3)^2\)
2. \(5s^{5}-70s^{4}+245s^{3}=5s^{3}(s^2-14s+49)=5s^{3}(s-7)^2\)
3. \(12b^{20}-75b^{4}=3b^{4}(4b^{16}-25)=3b^{4}(2b^8+5)(2b^8-5)\)
4. \(-72b^{4}-168b^{3}-98b^{2}=-2b^{2}(36b^{2}+84b+49)=-2b^{2}(6b+7)^2\)
5. \(80x^{14}+40x^{9}+5x^{4}=5x^{4}(16x^{10}+8x^5+1)=5x^{4}(4x^5+1)^2\)
6. \(-27q^{8}-36q^{5}-12q^{2}=-3q^{2}(9q^{6}+12q^3+4)=-3q^{2}(3q^3+2)^2\)
7. \(-16a^{6}+56a^{5}-49a^{4}=-a^{4}(16a^{2}-56a+49)=-a^{4}(4a-7)^2\)
8. \(2q^{4}+36q^{3}+162q^{2}=2q^{2}(q^2+18q+81)=2q^{2}(q+9)^2\)
9. \(2x^{6}-8x^{4}=2x^{4}(x^2-4)=2x^{4}(x-2)(x+2)\)
10. \(-2a^{6}+8a^{4}=-2a^{4}(a^2-4)=-2a^{4}(a-2)(a+2)\)
11. \(80a^{11}-120a^{7}p+45a^{3}p^2=5a^{3}(16a^{8}-24a^4p+9p^2)=5a^{3}(4a^4-3p)^2\)
12. \(-2s^{5}+28s^{4}-98s^{3}=-2s^{3}(s^2-14s+49)=-2s^{3}(s-7)^2\)