Ontbinden in factoren (2)

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

1. \(54x^{6}+36x^{5}+6x^{4}\)
2. \(-27s^{5}+75s^{3}\)
3. \(-45b^{11}-30b^{7}y-5b^{3}y^2\)
4. \(-45p^{5}-30p^{4}-5p^{3}\)
5. \(-45p^{13}-120p^{9}-80p^{5}\)
6. \(-3q^{4}+3q^{2}\)
7. \(9y^{13}+24y^{9}+16y^{5}\)
8. \(5y^{5}-80y^{3}\)
9. \(-16s^{6}+s^{4}\)
10. \(-16x^{13}-24x^{9}-9x^{5}\)
11. \(-150a^{7}+120a^{5}b-24a^{3}b^2\)
12. \(4a^{13}+4a^{8}p+a^{3}p^2\)

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

Verbetersleutel

1. \(54x^{6}+36x^{5}+6x^{4}=6x^{4}(9x^{2}+6x+1)=6x^{4}(3x+1)^2\)
2. \(-27s^{5}+75s^{3}=-3s^{3}(9s^{2}-25)=-3s^{3}(3s+5)(3s-5)\)
3. \(-45b^{11}-30b^{7}y-5b^{3}y^2=-5b^{3}(9b^{8}+6b^4y+y^2)=-5b^{3}(3b^4+y)^2\)
4. \(-45p^{5}-30p^{4}-5p^{3}=-5p^{3}(9p^{2}+6p+1)=-5p^{3}(3p+1)^2\)
5. \(-45p^{13}-120p^{9}-80p^{5}=-5p^{5}(9p^{8}+24p^4+16)=-5p^{5}(3p^4+4)^2\)
6. \(-3q^{4}+3q^{2}=-3q^{2}(q^2-1)=-3q^{2}(q+1)(q-1)\)
7. \(9y^{13}+24y^{9}+16y^{5}=y^{5}(9y^{8}+24y^4+16)=y^{5}(3y^4+4)^2\)
8. \(5y^{5}-80y^{3}=5y^{3}(y^2-16)=5y^{3}(y+4)(y-4)\)
9. \(-16s^{6}+s^{4}=-s^{4}(16s^{2}-1)=-s^{4}(4s+1)(4s-1)\)
10. \(-16x^{13}-24x^{9}-9x^{5}=-x^{5}(16x^{8}+24x^4+9)=-x^{5}(4x^4+3)^2\)
11. \(-150a^{7}+120a^{5}b-24a^{3}b^2=-6a^{3}(25a^{4}-20a^2b+4b^2)=-6a^{3}(5a^2-2b)^2\)
12. \(4a^{13}+4a^{8}p+a^{3}p^2=a^{3}(4a^{10}+4a^5p+p^2)=a^{3}(2a^5+p)^2\)