Ontbinden in factoren (2)

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

1. \(-54q^{15}+6q^{3}\)
2. \(12s^{16}-147s^{4}\)
3. \(-96b^{13}+6b^{3}\)
4. \(x^{5}+16x^{4}+64x^{3}\)
5. \(-8y^{4}+18y^{2}\)
6. \(20q^{10}+20q^{6}y+5q^{2}y^2\)
7. \(125p^{9}-200p^{6}+80p^{3}\)
8. \(-45a^{7}+80a^{5}\)
9. \(-96x^{4}-336x^{3}-294x^{2}\)
10. \(-75x^{15}+210x^{10}y-147x^{5}y^2\)
11. \(3a^{5}-24a^{4}+48a^{3}\)
12. \(-8p^{5}+98p^{3}\)

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

Verbetersleutel

1. \(-54q^{15}+6q^{3}=-6q^{3}(9q^{12}-1)=-6q^{3}(3q^6+1)(3q^6-1)\)
2. \(12s^{16}-147s^{4}=3s^{4}(4s^{12}-49)=3s^{4}(2s^6+7)(2s^6-7)\)
3. \(-96b^{13}+6b^{3}=-6b^{3}(16b^{10}-1)=-6b^{3}(4b^5+1)(4b^5-1)\)
4. \(x^{5}+16x^{4}+64x^{3}=x^{3}(x^2+16x+64)=x^{3}(x+8)^2\)
5. \(-8y^{4}+18y^{2}=-2y^{2}(4y^{2}-9)=-2y^{2}(2y+3)(2y-3)\)
6. \(20q^{10}+20q^{6}y+5q^{2}y^2=5q^{2}(4q^{8}+4q^4y+y^2)=5q^{2}(2q^4+y)^2\)
7. \(125p^{9}-200p^{6}+80p^{3}=5p^{3}(25p^{6}-40p^3+16)=5p^{3}(5p^3-4)^2\)
8. \(-45a^{7}+80a^{5}=-5a^{5}(9a^{2}-16)=-5a^{5}(3a+4)(3a-4)\)
9. \(-96x^{4}-336x^{3}-294x^{2}=-6x^{2}(16x^{2}+56x+49)=-6x^{2}(4x+7)^2\)
10. \(-75x^{15}+210x^{10}y-147x^{5}y^2=-3x^{5}(25x^{10}-70x^5y+49y^2)=-3x^{5}(5x^5-7y)^2\)
11. \(3a^{5}-24a^{4}+48a^{3}=3a^{3}(a^2-8a+16)=3a^{3}(a-4)^2\)
12. \(-8p^{5}+98p^{3}=-2p^{3}(4p^{2}-49)=-2p^{3}(2p+7)(2p-7)\)