Ontbinden in factoren (2)

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

1. \(-16q^{15}-40q^{10}x-25q^{5}x^2\)
2. \(45y^{4}-320y^{2}\)
3. \(48p^{9}+168p^{7}+147p^{5}\)
4. \(-5s^{7}+125s^{5}\)
5. \(5p^{7}+60p^{6}+180p^{5}\)
6. \(-20a^{12}+125a^{2}\)
7. \(-72p^{11}+98p^{3}\)
8. \(-12s^{12}-60s^{8}-75s^{4}\)
9. \(6q^{7}+12q^{6}+6q^{5}\)
10. \(-3q^{5}+147q^{3}\)
11. \(75q^{13}-210q^{8}x+147q^{3}x^2\)
12. \(-80b^{15}-40b^{10}s-5b^{5}s^2\)

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

Verbetersleutel

1. \(-16q^{15}-40q^{10}x-25q^{5}x^2=-q^{5}(16q^{10}+40q^5x+25x^2)=-q^{5}(4q^5+5x)^2\)
2. \(45y^{4}-320y^{2}=5y^{2}(9y^{2}-64)=5y^{2}(3y+8)(3y-8)\)
3. \(48p^{9}+168p^{7}+147p^{5}=3p^{5}(16p^{4}+56p^2+49)=3p^{5}(4p^2+7)^2\)
4. \(-5s^{7}+125s^{5}=-5s^{5}(s^2-25)=-5s^{5}(s-5)(s+5)\)
5. \(5p^{7}+60p^{6}+180p^{5}=5p^{5}(p^2+12p+36)=5p^{5}(p+6)^2\)
6. \(-20a^{12}+125a^{2}=-5a^{2}(4a^{10}-25)=-5a^{2}(2a^5+5)(2a^5-5)\)
7. \(-72p^{11}+98p^{3}=-2p^{3}(36p^{8}-49)=-2p^{3}(6p^4+7)(6p^4-7)\)
8. \(-12s^{12}-60s^{8}-75s^{4}=-3s^{4}(4s^{8}+20s^4+25)=-3s^{4}(2s^4+5)^2\)
9. \(6q^{7}+12q^{6}+6q^{5}=6q^{5}(q^2+2q+1)=6q^{5}(q+1)^2\)
10. \(-3q^{5}+147q^{3}=-3q^{3}(q^2-49)=-3q^{3}(q+7)(q-7)\)
11. \(75q^{13}-210q^{8}x+147q^{3}x^2=3q^{3}(25q^{10}-70q^5x+49x^2)=3q^{3}(5q^5-7x)^2\)
12. \(-80b^{15}-40b^{10}s-5b^{5}s^2=-5b^{5}(16b^{10}+8b^5s+s^2)=-5b^{5}(4b^5+s)^2\)