Ontbinden in factoren (2)

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

1. \(-3p^{5}+192p^{3}\)
2. \(216y^{21}-294y^{5}\)
3. \(4q^{6}-9q^{4}\)
4. \(-24q^{6}-120q^{5}-150q^{4}\)
5. \(-3y^{5}+42y^{4}-147y^{3}\)
6. \(-125x^{9}+200x^{7}y-80x^{5}y^2\)
7. \(-150s^{17}+24s^{5}\)
8. \(-192a^{12}-48a^{7}-3a^{2}\)
9. \(12a^{13}+12a^{8}+3a^{3}\)
10. \(18s^{10}-24s^{7}y+8s^{4}y^2\)
11. \(-180q^{4}+300q^{3}-125q^{2}\)
12. \(-180p^{14}+5p^{4}\)

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

Verbetersleutel

1. \(-3p^{5}+192p^{3}=-3p^{3}(p^2-64)=-3p^{3}(p-8)(p+8)\)
2. \(216y^{21}-294y^{5}=6y^{5}(36y^{16}-49)=6y^{5}(6y^8+7)(6y^8-7)\)
3. \(4q^{6}-9q^{4}=q^{4}(4q^{2}-9)=q^{4}(2q+3)(2q-3)\)
4. \(-24q^{6}-120q^{5}-150q^{4}=-6q^{4}(4q^{2}+20q+25)=-6q^{4}(2q+5)^2\)
5. \(-3y^{5}+42y^{4}-147y^{3}=-3y^{3}(y^2-14y+49)=-3y^{3}(y-7)^2\)
6. \(-125x^{9}+200x^{7}y-80x^{5}y^2=-5x^{5}(25x^{4}-40x^2y+16y^2)=-5x^{5}(5x^2-4y)^2\)
7. \(-150s^{17}+24s^{5}=-6s^{5}(25s^{12}-4)=-6s^{5}(5s^6+2)(5s^6-2)\)
8. \(-192a^{12}-48a^{7}-3a^{2}=-3a^{2}(64a^{10}+16a^5+1)=-3a^{2}(8a^5+1)^2\)
9. \(12a^{13}+12a^{8}+3a^{3}=3a^{3}(4a^{10}+4a^5+1)=3a^{3}(2a^5+1)^2\)
10. \(18s^{10}-24s^{7}y+8s^{4}y^2=2s^{4}(9s^{6}-12s^3y+4y^2)=2s^{4}(3s^3-2y)^2\)
11. \(-180q^{4}+300q^{3}-125q^{2}=-5q^{2}(36q^{2}-60q+25)=-5q^{2}(6q-5)^2\)
12. \(-180p^{14}+5p^{4}=-5p^{4}(36p^{10}-1)=-5p^{4}(6p^5+1)(6p^5-1)\)