Ontbinden in factoren (2)

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

1. \(-150b^{5}+420b^{4}-294b^{3}\)
2. \(25x^{17}-x^{3}\)
3. \(-294q^{4}+252q^{3}-54q^{2}\)
4. \(-50y^{4}+18y^{2}\)
5. \(24x^{6}+168x^{5}+294x^{4}\)
6. \(-x^{4}+25x^{2}\)
7. \(6q^{5}-384q^{3}\)
8. \(-128b^{11}-160b^{8}s-50b^{5}s^2\)
9. \(-72a^{21}+50a^{5}\)
10. \(-45x^{17}+80x^{5}\)
11. \(p^{4}-8p^{3}+16p^{2}\)
12. \(x^{6}-25x^{4}\)

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

Verbetersleutel

1. \(-150b^{5}+420b^{4}-294b^{3}=-6b^{3}(25b^{2}-70b+49)=-6b^{3}(5b-7)^2\)
2. \(25x^{17}-x^{3}=x^{3}(25x^{14}-1)=x^{3}(5x^7+1)(5x^7-1)\)
3. \(-294q^{4}+252q^{3}-54q^{2}=-6q^{2}(49q^{2}-42q+9)=-6q^{2}(7q-3)^2\)
4. \(-50y^{4}+18y^{2}=-2y^{2}(25y^{2}-9)=-2y^{2}(5y+3)(5y-3)\)
5. \(24x^{6}+168x^{5}+294x^{4}=6x^{4}(4x^{2}+28x+49)=6x^{4}(2x+7)^2\)
6. \(-x^{4}+25x^{2}=-x^{2}(x^2-25)=-x^{2}(x+5)(x-5)\)
7. \(6q^{5}-384q^{3}=6q^{3}(q^2-64)=6q^{3}(q-8)(q+8)\)
8. \(-128b^{11}-160b^{8}s-50b^{5}s^2=-2b^{5}(64b^{6}+80b^3s+25s^2)=-2b^{5}(8b^3+5s)^2\)
9. \(-72a^{21}+50a^{5}=-2a^{5}(36a^{16}-25)=-2a^{5}(6a^8+5)(6a^8-5)\)
10. \(-45x^{17}+80x^{5}=-5x^{5}(9x^{12}-16)=-5x^{5}(3x^6+4)(3x^6-4)\)
11. \(p^{4}-8p^{3}+16p^{2}=p^{2}(p^2-8p+16)=p^{2}(p-4)^2\)
12. \(x^{6}-25x^{4}=x^{4}(x^2-25)=x^{4}(x-5)(x+5)\)