Ontbinden in factoren (2)

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

1. \(-180s^{6}+125s^{4}\)
2. \(-6p^{7}-72p^{6}-216p^{5}\)
3. \(294x^{15}+168x^{10}+24x^{5}\)
4. \(-5y^{5}+320y^{3}\)
5. \(-180a^{7}+5a^{5}\)
6. \(-147a^{6}-42a^{4}q-3a^{2}q^2\)
7. \(180x^{10}+300x^{6}+125x^{2}\)
8. \(-45b^{6}-30b^{5}-5b^{4}\)
9. \(-48b^{9}-24b^{7}-3b^{5}\)
10. \(-18b^{5}+24b^{4}-8b^{3}\)
11. \(5a^{7}-80a^{5}\)
12. \(75y^{6}-270y^{5}+243y^{4}\)

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

Verbetersleutel

1. \(-180s^{6}+125s^{4}=-5s^{4}(36s^{2}-25)=-5s^{4}(6s+5)(6s-5)\)
2. \(-6p^{7}-72p^{6}-216p^{5}=-6p^{5}(p^2+12p+36)=-6p^{5}(p+6)^2\)
3. \(294x^{15}+168x^{10}+24x^{5}=6x^{5}(49x^{10}+28x^5+4)=6x^{5}(7x^5+2)^2\)
4. \(-5y^{5}+320y^{3}=-5y^{3}(y^2-64)=-5y^{3}(y-8)(y+8)\)
5. \(-180a^{7}+5a^{5}=-5a^{5}(36a^{2}-1)=-5a^{5}(6a+1)(6a-1)\)
6. \(-147a^{6}-42a^{4}q-3a^{2}q^2=-3a^{2}(49a^{4}+14a^2q+q^2)=-3a^{2}(7a^2+q)^2\)
7. \(180x^{10}+300x^{6}+125x^{2}=5x^{2}(36x^{8}+60x^4+25)=5x^{2}(6x^4+5)^2\)
8. \(-45b^{6}-30b^{5}-5b^{4}=-5b^{4}(9b^{2}+6b+1)=-5b^{4}(3b+1)^2\)
9. \(-48b^{9}-24b^{7}-3b^{5}=-3b^{5}(16b^{4}+8b^2+1)=-3b^{5}(4b^2+1)^2\)
10. \(-18b^{5}+24b^{4}-8b^{3}=-2b^{3}(9b^{2}-12b+4)=-2b^{3}(3b-2)^2\)
11. \(5a^{7}-80a^{5}=5a^{5}(a^2-16)=5a^{5}(a+4)(a-4)\)
12. \(75y^{6}-270y^{5}+243y^{4}=3y^{4}(25y^{2}-90y+81)=3y^{4}(5y-9)^2\)