Ontbinden in factoren (2)

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

1. \(-6b^{7}-12b^{6}-6b^{5}\)
2. \(6y^{7}-108y^{6}+486y^{5}\)
3. \(54b^{7}+72b^{5}y+24b^{3}y^2\)
4. \(-64x^{4}-16x^{3}-x^{2}\)
5. \(320b^{10}+240b^{6}p+45b^{2}p^2\)
6. \(-b^{6}-2b^{5}-b^{4}\)
7. \(96s^{6}-144s^{5}+54s^{4}\)
8. \(-72a^{8}-24a^{6}-2a^{4}\)
9. \(-128s^{9}-32s^{6}-2s^{3}\)
10. \(8b^{7}+8b^{5}s+2b^{3}s^2\)
11. \(-36b^{18}+25b^{2}\)
12. \(27x^{7}-36x^{6}+12x^{5}\)

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

Verbetersleutel

1. \(-6b^{7}-12b^{6}-6b^{5}=-6b^{5}(b^2+2b+1)=-6b^{5}(b+1)^2\)
2. \(6y^{7}-108y^{6}+486y^{5}=6y^{5}(y^2-18y+81)=6y^{5}(y-9)^2\)
3. \(54b^{7}+72b^{5}y+24b^{3}y^2=6b^{3}(9b^{4}+12b^2y+4y^2)=6b^{3}(3b^2+2y)^2\)
4. \(-64x^{4}-16x^{3}-x^{2}=-x^{2}(64x^{2}+16x+1)=-x^{2}(8x+1)^2\)
5. \(320b^{10}+240b^{6}p+45b^{2}p^2=5b^{2}(64b^{8}+48b^4p+9p^2)=5b^{2}(8b^4+3p)^2\)
6. \(-b^{6}-2b^{5}-b^{4}=-b^{4}(b^2+2b+1)=-b^{4}(b+1)^2\)
7. \(96s^{6}-144s^{5}+54s^{4}=6s^{4}(16s^{2}-24s+9)=6s^{4}(4s-3)^2\)
8. \(-72a^{8}-24a^{6}-2a^{4}=-2a^{4}(36a^{4}+12a^2+1)=-2a^{4}(6a^2+1)^2\)
9. \(-128s^{9}-32s^{6}-2s^{3}=-2s^{3}(64s^{6}+16s^3+1)=-2s^{3}(8s^3+1)^2\)
10. \(8b^{7}+8b^{5}s+2b^{3}s^2=2b^{3}(4b^{4}+4b^2s+s^2)=2b^{3}(2b^2+s)^2\)
11. \(-36b^{18}+25b^{2}=-b^{2}(36b^{16}-25)=-b^{2}(6b^8+5)(6b^8-5)\)
12. \(27x^{7}-36x^{6}+12x^{5}=3x^{5}(9x^{2}-12x+4)=3x^{5}(3x-2)^2\)