Ontbinden in factoren (2)

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

1. \(8x^{16}-98x^{4}\)
2. \(27q^{6}-147q^{4}\)
3. \(54x^{15}-96x^{5}\)
4. \(18b^{6}-24b^{5}+8b^{4}\)
5. \(-24p^{12}-24p^{7}x-6p^{2}x^2\)
6. \(p^{5}-4p^{3}\)
7. \(q^{4}-49q^{2}\)
8. \(-384b^{13}-96b^{9}-6b^{5}\)
9. \(-49a^{9}-56a^{6}x-16a^{3}x^2\)
10. \(-50a^{4}+8a^{2}\)
11. \(80p^{7}-125p^{5}\)
12. \(-49a^{13}+84a^{9}s-36a^{5}s^2\)

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

Verbetersleutel

1. \(8x^{16}-98x^{4}=2x^{4}(4x^{12}-49)=2x^{4}(2x^6+7)(2x^6-7)\)
2. \(27q^{6}-147q^{4}=3q^{4}(9q^{2}-49)=3q^{4}(3q+7)(3q-7)\)
3. \(54x^{15}-96x^{5}=6x^{5}(9x^{10}-16)=6x^{5}(3x^5+4)(3x^5-4)\)
4. \(18b^{6}-24b^{5}+8b^{4}=2b^{4}(9b^{2}-12b+4)=2b^{4}(3b-2)^2\)
5. \(-24p^{12}-24p^{7}x-6p^{2}x^2=-6p^{2}(4p^{10}+4p^5x+x^2)=-6p^{2}(2p^5+x)^2\)
6. \(p^{5}-4p^{3}=p^{3}(p^2-4)=p^{3}(p+2)(p-2)\)
7. \(q^{4}-49q^{2}=q^{2}(q^2-49)=q^{2}(q+7)(q-7)\)
8. \(-384b^{13}-96b^{9}-6b^{5}=-6b^{5}(64b^{8}+16b^4+1)=-6b^{5}(8b^4+1)^2\)
9. \(-49a^{9}-56a^{6}x-16a^{3}x^2=-a^{3}(49a^{6}+56a^3x+16x^2)=-a^{3}(7a^3+4x)^2\)
10. \(-50a^{4}+8a^{2}=-2a^{2}(25a^{2}-4)=-2a^{2}(5a+2)(5a-2)\)
11. \(80p^{7}-125p^{5}=5p^{5}(16p^{2}-25)=5p^{5}(4p+5)(4p-5)\)
12. \(-49a^{13}+84a^{9}s-36a^{5}s^2=-a^{5}(49a^{8}-84a^4s+36s^2)=-a^{5}(7a^4-6s)^2\)