Ontbinden in factoren (2)

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

1. \(-6q^{5}+54q^{3}\)
2. \(-98y^{5}+168y^{4}-72y^{3}\)
3. \(-4p^{8}-4p^{6}-p^{4}\)
4. \(b^{5}-2b^{4}+b^{3}\)
5. \(-12b^{15}-12b^{10}q-3b^{5}q^2\)
6. \(x^{7}-64x^{5}\)
7. \(6q^{7}+96q^{6}+384q^{5}\)
8. \(s^{5}-36s^{3}\)
9. \(20y^{7}-125y^{5}\)
10. \(98s^{7}+140s^{6}+50s^{5}\)
11. \(8b^{7}+8b^{6}+2b^{5}\)
12. \(9a^{11}-30a^{7}p+25a^{3}p^2\)

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

Verbetersleutel

1. \(-6q^{5}+54q^{3}=-6q^{3}(q^2-9)=-6q^{3}(q+3)(q-3)\)
2. \(-98y^{5}+168y^{4}-72y^{3}=-2y^{3}(49y^{2}-84y+36)=-2y^{3}(7y-6)^2\)
3. \(-4p^{8}-4p^{6}-p^{4}=-p^{4}(4p^{4}+4p^2+1)=-p^{4}(2p^2+1)^2\)
4. \(b^{5}-2b^{4}+b^{3}=b^{3}(b^2-2b+1)=b^{3}(b-1)^2\)
5. \(-12b^{15}-12b^{10}q-3b^{5}q^2=-3b^{5}(4b^{10}+4b^5q+q^2)=-3b^{5}(2b^5+q)^2\)
6. \(x^{7}-64x^{5}=x^{5}(x^2-64)=x^{5}(x+8)(x-8)\)
7. \(6q^{7}+96q^{6}+384q^{5}=6q^{5}(q^2+16q+64)=6q^{5}(q+8)^2\)
8. \(s^{5}-36s^{3}=s^{3}(s^2-36)=s^{3}(s+6)(s-6)\)
9. \(20y^{7}-125y^{5}=5y^{5}(4y^{2}-25)=5y^{5}(2y+5)(2y-5)\)
10. \(98s^{7}+140s^{6}+50s^{5}=2s^{5}(49s^{2}+70s+25)=2s^{5}(7s+5)^2\)
11. \(8b^{7}+8b^{6}+2b^{5}=2b^{5}(4b^{2}+4b+1)=2b^{5}(2b+1)^2\)
12. \(9a^{11}-30a^{7}p+25a^{3}p^2=a^{3}(9a^{8}-30a^4p+25p^2)=a^{3}(3a^4-5p)^2\)