Ontbinden in factoren (2)

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

1. \(-75p^{8}-30p^{6}-3p^{4}\)
2. \(-3s^{7}+75s^{5}\)
3. \(2s^{5}+12s^{4}+18s^{3}\)
4. \(125q^{4}-245q^{2}\)
5. \(x^{4}-4x^{2}\)
6. \(-180s^{14}+300s^{9}x-125s^{4}x^2\)
7. \(72a^{15}-50a^{3}\)
8. \(-8p^{12}-8p^{7}x-2p^{2}x^2\)
9. \(-6y^{7}-48y^{6}-96y^{5}\)
10. \(-6x^{6}+36x^{5}-54x^{4}\)
11. \(-2s^{7}-24s^{6}-72s^{5}\)
12. \(50s^{5}-72s^{3}\)

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

Verbetersleutel

1. \(-75p^{8}-30p^{6}-3p^{4}=-3p^{4}(25p^{4}+10p^2+1)=-3p^{4}(5p^2+1)^2\)
2. \(-3s^{7}+75s^{5}=-3s^{5}(s^2-25)=-3s^{5}(s+5)(s-5)\)
3. \(2s^{5}+12s^{4}+18s^{3}=2s^{3}(s^2+6s+9)=2s^{3}(s+3)^2\)
4. \(125q^{4}-245q^{2}=5q^{2}(25q^{2}-49)=5q^{2}(5q+7)(5q-7)\)
5. \(x^{4}-4x^{2}=x^{2}(x^2-4)=x^{2}(x-2)(x+2)\)
6. \(-180s^{14}+300s^{9}x-125s^{4}x^2=-5s^{4}(36s^{10}-60s^5x+25x^2)=-5s^{4}(6s^5-5x)^2\)
7. \(72a^{15}-50a^{3}=2a^{3}(36a^{12}-25)=2a^{3}(6a^6+5)(6a^6-5)\)
8. \(-8p^{12}-8p^{7}x-2p^{2}x^2=-2p^{2}(4p^{10}+4p^5x+x^2)=-2p^{2}(2p^5+x)^2\)
9. \(-6y^{7}-48y^{6}-96y^{5}=-6y^{5}(y^2+8y+16)=-6y^{5}(y+4)^2\)
10. \(-6x^{6}+36x^{5}-54x^{4}=-6x^{4}(x^2-6x+9)=-6x^{4}(x-3)^2\)
11. \(-2s^{7}-24s^{6}-72s^{5}=-2s^{5}(s^2+12s+36)=-2s^{5}(s+6)^2\)
12. \(50s^{5}-72s^{3}=2s^{3}(25s^{2}-36)=2s^{3}(5s+6)(5s-6)\)