Ontbinden in factoren (2)

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

1. \(-q^{5}-4q^{4}-4q^{3}\)
2. \(4p^{10}+20p^{6}+25p^{2}\)
3. \(-80y^{4}-40y^{3}-5y^{2}\)
4. \(6q^{5}-96q^{3}\)
5. \(36p^{13}-25p^{3}\)
6. \(24b^{9}+24b^{6}+6b^{3}\)
7. \(128y^{13}-224y^{8}+98y^{3}\)
8. \(-5s^{6}+180s^{4}\)
9. \(32s^{5}-98s^{3}\)
10. \(-2b^{6}-4b^{5}-2b^{4}\)
11. \(96s^{14}+48s^{9}x+6s^{4}x^2\)
12. \(-2a^{4}-16a^{3}-32a^{2}\)

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

Verbetersleutel

1. \(-q^{5}-4q^{4}-4q^{3}=-q^{3}(q^2+4q+4)=-q^{3}(q+2)^2\)
2. \(4p^{10}+20p^{6}+25p^{2}=p^{2}(4p^{8}+20p^4+25)=p^{2}(2p^4+5)^2\)
3. \(-80y^{4}-40y^{3}-5y^{2}=-5y^{2}(16y^{2}+8y+1)=-5y^{2}(4y+1)^2\)
4. \(6q^{5}-96q^{3}=6q^{3}(q^2-16)=6q^{3}(q-4)(q+4)\)
5. \(36p^{13}-25p^{3}=p^{3}(36p^{10}-25)=p^{3}(6p^5+5)(6p^5-5)\)
6. \(24b^{9}+24b^{6}+6b^{3}=6b^{3}(4b^{6}+4b^3+1)=6b^{3}(2b^3+1)^2\)
7. \(128y^{13}-224y^{8}+98y^{3}=2y^{3}(64y^{10}-112y^5+49)=2y^{3}(8y^5-7)^2\)
8. \(-5s^{6}+180s^{4}=-5s^{4}(s^2-36)=-5s^{4}(s-6)(s+6)\)
9. \(32s^{5}-98s^{3}=2s^{3}(16s^{2}-49)=2s^{3}(4s+7)(4s-7)\)
10. \(-2b^{6}-4b^{5}-2b^{4}=-2b^{4}(b^2+2b+1)=-2b^{4}(b+1)^2\)
11. \(96s^{14}+48s^{9}x+6s^{4}x^2=6s^{4}(16s^{10}+8s^5x+x^2)=6s^{4}(4s^5+x)^2\)
12. \(-2a^{4}-16a^{3}-32a^{2}=-2a^{2}(a^2+8a+16)=-2a^{2}(a+4)^2\)