Ontbinden in factoren (2)

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

1. \(-9b^{4}-42b^{3}-49b^{2}\)
2. \(147q^{5}+126q^{4}+27q^{3}\)
3. \(6q^{7}-96q^{5}\)
4. \(y^{7}-16y^{6}+64y^{5}\)
5. \(-2p^{5}+32p^{4}-128p^{3}\)
6. \(-108y^{4}+75y^{2}\)
7. \(-12q^{11}+3q^{5}\)
8. \(3p^{4}-12p^{2}\)
9. \(-25a^{7}+36a^{5}\)
10. \(-20s^{7}+5s^{5}\)
11. \(-72p^{13}-24p^{9}-2p^{5}\)
12. \(-18p^{10}-24p^{7}y-8p^{4}y^2\)

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

Verbetersleutel

1. \(-9b^{4}-42b^{3}-49b^{2}=-b^{2}(9b^{2}+42b+49)=-b^{2}(3b+7)^2\)
2. \(147q^{5}+126q^{4}+27q^{3}=3q^{3}(49q^{2}+42q+9)=3q^{3}(7q+3)^2\)
3. \(6q^{7}-96q^{5}=6q^{5}(q^2-16)=6q^{5}(q+4)(q-4)\)
4. \(y^{7}-16y^{6}+64y^{5}=y^{5}(y^2-16y+64)=y^{5}(y-8)^2\)
5. \(-2p^{5}+32p^{4}-128p^{3}=-2p^{3}(p^2-16p+64)=-2p^{3}(p-8)^2\)
6. \(-108y^{4}+75y^{2}=-3y^{2}(36y^{2}-25)=-3y^{2}(6y+5)(6y-5)\)
7. \(-12q^{11}+3q^{5}=-3q^{5}(4q^{6}-1)=-3q^{5}(2q^3+1)(2q^3-1)\)
8. \(3p^{4}-12p^{2}=3p^{2}(p^2-4)=3p^{2}(p-2)(p+2)\)
9. \(-25a^{7}+36a^{5}=-a^{5}(25a^{2}-36)=-a^{5}(5a+6)(5a-6)\)
10. \(-20s^{7}+5s^{5}=-5s^{5}(4s^{2}-1)=-5s^{5}(2s+1)(2s-1)\)
11. \(-72p^{13}-24p^{9}-2p^{5}=-2p^{5}(36p^{8}+12p^4+1)=-2p^{5}(6p^4+1)^2\)
12. \(-18p^{10}-24p^{7}y-8p^{4}y^2=-2p^{4}(9p^{6}+12p^3y+4y^2)=-2p^{4}(3p^3+2y)^2\)