Ontbinden in factoren (2)

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

1. \(2y^{4}-32y^{3}+128y^{2}\)
2. \(-9p^{5}-48p^{4}-64p^{3}\)
3. \(-192s^{9}-48s^{7}-3s^{5}\)
4. \(-72y^{5}+2y^{3}\)
5. \(-48p^{13}+3p^{5}\)
6. \(-125p^{6}+350p^{5}-245p^{4}\)
7. \(-s^{5}-2s^{4}-s^{3}\)
8. \(-6x^{5}+6x^{3}\)
9. \(75a^{12}+30a^{8}b+3a^{4}b^2\)
10. \(b^{4}+4b^{3}+4b^{2}\)
11. \(245a^{5}+210a^{4}+45a^{3}\)
12. \(8y^{7}-50y^{5}\)

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

Verbetersleutel

1. \(2y^{4}-32y^{3}+128y^{2}=2y^{2}(y^2-16y+64)=2y^{2}(y-8)^2\)
2. \(-9p^{5}-48p^{4}-64p^{3}=-p^{3}(9p^{2}+48p+64)=-p^{3}(3p+8)^2\)
3. \(-192s^{9}-48s^{7}-3s^{5}=-3s^{5}(64s^{4}+16s^2+1)=-3s^{5}(8s^2+1)^2\)
4. \(-72y^{5}+2y^{3}=-2y^{3}(36y^{2}-1)=-2y^{3}(6y+1)(6y-1)\)
5. \(-48p^{13}+3p^{5}=-3p^{5}(16p^{8}-1)=-3p^{5}(4p^4+1)(4p^4-1)\)
6. \(-125p^{6}+350p^{5}-245p^{4}=-5p^{4}(25p^{2}-70p+49)=-5p^{4}(5p-7)^2\)
7. \(-s^{5}-2s^{4}-s^{3}=-s^{3}(s^2+2s+1)=-s^{3}(s+1)^2\)
8. \(-6x^{5}+6x^{3}=-6x^{3}(x^2-1)=-6x^{3}(x+1)(x-1)\)
9. \(75a^{12}+30a^{8}b+3a^{4}b^2=3a^{4}(25a^{8}+10a^4b+b^2)=3a^{4}(5a^4+b)^2\)
10. \(b^{4}+4b^{3}+4b^{2}=b^{2}(b^2+4b+4)=b^{2}(b+2)^2\)
11. \(245a^{5}+210a^{4}+45a^{3}=5a^{3}(49a^{2}+42a+9)=5a^{3}(7a+3)^2\)
12. \(8y^{7}-50y^{5}=2y^{5}(4y^{2}-25)=2y^{5}(2y+5)(2y-5)\)