Ontbinden in factoren (2)

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

1. \(32q^{9}+48q^{7}+18q^{5}\)
2. \(-125q^{13}-100q^{9}s-20q^{5}s^2\)
3. \(12s^{6}+12s^{5}+3s^{4}\)
4. \(2y^{5}-2y^{3}\)
5. \(180p^{13}-125p^{5}\)
6. \(-320y^{13}+560y^{9}-245y^{5}\)
7. \(-150p^{12}-60p^{8}y-6p^{4}y^2\)
8. \(-150s^{9}-360s^{7}-216s^{5}\)
9. \(-45b^{6}+150b^{4}x-125b^{2}x^2\)
10. \(-147q^{12}-210q^{7}s-75q^{2}s^2\)
11. \(-5y^{6}+125y^{4}\)
12. \(8x^{5}+40x^{4}+50x^{3}\)

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

Verbetersleutel

1. \(32q^{9}+48q^{7}+18q^{5}=2q^{5}(16q^{4}+24q^2+9)=2q^{5}(4q^2+3)^2\)
2. \(-125q^{13}-100q^{9}s-20q^{5}s^2=-5q^{5}(25q^{8}+20q^4s+4s^2)=-5q^{5}(5q^4+2s)^2\)
3. \(12s^{6}+12s^{5}+3s^{4}=3s^{4}(4s^{2}+4s+1)=3s^{4}(2s+1)^2\)
4. \(2y^{5}-2y^{3}=2y^{3}(y^2-1)=2y^{3}(y+1)(y-1)\)
5. \(180p^{13}-125p^{5}=5p^{5}(36p^{8}-25)=5p^{5}(6p^4+5)(6p^4-5)\)
6. \(-320y^{13}+560y^{9}-245y^{5}=-5y^{5}(64y^{8}-112y^4+49)=-5y^{5}(8y^4-7)^2\)
7. \(-150p^{12}-60p^{8}y-6p^{4}y^2=-6p^{4}(25p^{8}+10p^4y+y^2)=-6p^{4}(5p^4+y)^2\)
8. \(-150s^{9}-360s^{7}-216s^{5}=-6s^{5}(25s^{4}+60s^2+36)=-6s^{5}(5s^2+6)^2\)
9. \(-45b^{6}+150b^{4}x-125b^{2}x^2=-5b^{2}(9b^{4}-30b^2x+25x^2)=-5b^{2}(3b^2-5x)^2\)
10. \(-147q^{12}-210q^{7}s-75q^{2}s^2=-3q^{2}(49q^{10}+70q^5s+25s^2)=-3q^{2}(7q^5+5s)^2\)
11. \(-5y^{6}+125y^{4}=-5y^{4}(y^2-25)=-5y^{4}(y+5)(y-5)\)
12. \(8x^{5}+40x^{4}+50x^{3}=2x^{3}(4x^{2}+20x+25)=2x^{3}(2x+5)^2\)