Ontbinden in factoren (2)

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

1. \(-96p^{12}-240p^{7}-150p^{2}\)
2. \(-49b^{10}-14b^{7}x-b^{4}x^2\)
3. \(-25x^{19}+16x^{5}\)
4. \(6p^{5}+48p^{4}+96p^{3}\)
5. \(5p^{7}-5p^{5}\)
6. \(-6b^{6}+294b^{4}\)
7. \(-4q^{5}+49q^{3}\)
8. \(-16y^{7}-56y^{6}-49y^{5}\)
9. \(108q^{15}-75q^{5}\)
10. \(45b^{4}-150b^{3}+125b^{2}\)
11. \(45a^{13}-60a^{9}q+20a^{5}q^2\)
12. \(12p^{8}-75p^{4}\)

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

Verbetersleutel

1. \(-96p^{12}-240p^{7}-150p^{2}=-6p^{2}(16p^{10}+40p^5+25)=-6p^{2}(4p^5+5)^2\)
2. \(-49b^{10}-14b^{7}x-b^{4}x^2=-b^{4}(49b^{6}+14b^3x+x^2)=-b^{4}(7b^3+x)^2\)
3. \(-25x^{19}+16x^{5}=-x^{5}(25x^{14}-16)=-x^{5}(5x^7+4)(5x^7-4)\)
4. \(6p^{5}+48p^{4}+96p^{3}=6p^{3}(p^2+8p+16)=6p^{3}(p+4)^2\)
5. \(5p^{7}-5p^{5}=5p^{5}(p^2-1)=5p^{5}(p-1)(p+1)\)
6. \(-6b^{6}+294b^{4}=-6b^{4}(b^2-49)=-6b^{4}(b+7)(b-7)\)
7. \(-4q^{5}+49q^{3}=-q^{3}(4q^{2}-49)=-q^{3}(2q+7)(2q-7)\)
8. \(-16y^{7}-56y^{6}-49y^{5}=-y^{5}(16y^{2}+56y+49)=-y^{5}(4y+7)^2\)
9. \(108q^{15}-75q^{5}=3q^{5}(36q^{10}-25)=3q^{5}(6q^5+5)(6q^5-5)\)
10. \(45b^{4}-150b^{3}+125b^{2}=5b^{2}(9b^{2}-30b+25)=5b^{2}(3b-5)^2\)
11. \(45a^{13}-60a^{9}q+20a^{5}q^2=5a^{5}(9a^{8}-12a^4q+4q^2)=5a^{5}(3a^4-2q)^2\)
12. \(12p^{8}-75p^{4}=3p^{4}(4p^{4}-25)=3p^{4}(2p^2+5)(2p^2-5)\)