Ontbinden in factoren (2)

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

1. \(-6y^{6}+24y^{4}\)
2. \(-125q^{6}-50q^{5}-5q^{4}\)
3. \(x^{4}-36x^{2}\)
4. \(-294x^{9}+504x^{7}-216x^{5}\)
5. \(5x^{7}-90x^{6}+405x^{5}\)
6. \(9x^{5}-49x^{3}\)
7. \(-294p^{6}+504p^{5}-216p^{4}\)
8. \(45a^{19}-5a^{5}\)
9. \(-25p^{11}-40p^{7}-16p^{3}\)
10. \(-18p^{7}+32p^{5}\)
11. \(-294b^{9}+504b^{6}x-216b^{3}x^2\)
12. \(x^{4}-64x^{2}\)

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

Verbetersleutel

1. \(-6y^{6}+24y^{4}=-6y^{4}(y^2-4)=-6y^{4}(y-2)(y+2)\)
2. \(-125q^{6}-50q^{5}-5q^{4}=-5q^{4}(25q^{2}+10q+1)=-5q^{4}(5q+1)^2\)
3. \(x^{4}-36x^{2}=x^{2}(x^2-36)=x^{2}(x-6)(x+6)\)
4. \(-294x^{9}+504x^{7}-216x^{5}=-6x^{5}(49x^{4}-84x^2+36)=-6x^{5}(7x^2-6)^2\)
5. \(5x^{7}-90x^{6}+405x^{5}=5x^{5}(x^2-18x+81)=5x^{5}(x-9)^2\)
6. \(9x^{5}-49x^{3}=x^{3}(9x^{2}-49)=x^{3}(3x+7)(3x-7)\)
7. \(-294p^{6}+504p^{5}-216p^{4}=-6p^{4}(49p^{2}-84p+36)=-6p^{4}(7p-6)^2\)
8. \(45a^{19}-5a^{5}=5a^{5}(9a^{14}-1)=5a^{5}(3a^7+1)(3a^7-1)\)
9. \(-25p^{11}-40p^{7}-16p^{3}=-p^{3}(25p^{8}+40p^4+16)=-p^{3}(5p^4+4)^2\)
10. \(-18p^{7}+32p^{5}=-2p^{5}(9p^{2}-16)=-2p^{5}(3p+4)(3p-4)\)
11. \(-294b^{9}+504b^{6}x-216b^{3}x^2=-6b^{3}(49b^{6}-84b^3x+36x^2)=-6b^{3}(7b^3-6x)^2\)
12. \(x^{4}-64x^{2}=x^{2}(x^2-64)=x^{2}(x-8)(x+8)\)