Ontbinden in factoren (2)

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

1. \(-245b^{7}-350b^{5}-125b^{3}\)
2. \(6p^{6}+108p^{5}+486p^{4}\)
3. \(-b^{7}+12b^{6}-36b^{5}\)
4. \(-27a^{12}+12a^{2}\)
5. \(2s^{5}-2s^{3}\)
6. \(8y^{15}+24y^{10}+18y^{5}\)
7. \(9b^{15}-b^{5}\)
8. \(-2b^{7}+50b^{5}\)
9. \(-18q^{7}+98q^{5}\)
10. \(50b^{6}-18b^{4}\)
11. \(-294a^{10}+504a^{7}s-216a^{4}s^2\)
12. \(98x^{5}+224x^{4}+128x^{3}\)

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

Verbetersleutel

1. \(-245b^{7}-350b^{5}-125b^{3}=-5b^{3}(49b^{4}+70b^2+25)=-5b^{3}(7b^2+5)^2\)
2. \(6p^{6}+108p^{5}+486p^{4}=6p^{4}(p^2+18p+81)=6p^{4}(p+9)^2\)
3. \(-b^{7}+12b^{6}-36b^{5}=-b^{5}(b^2-12b+36)=-b^{5}(b-6)^2\)
4. \(-27a^{12}+12a^{2}=-3a^{2}(9a^{10}-4)=-3a^{2}(3a^5+2)(3a^5-2)\)
5. \(2s^{5}-2s^{3}=2s^{3}(s^2-1)=2s^{3}(s-1)(s+1)\)
6. \(8y^{15}+24y^{10}+18y^{5}=2y^{5}(4y^{10}+12y^5+9)=2y^{5}(2y^5+3)^2\)
7. \(9b^{15}-b^{5}=b^{5}(9b^{10}-1)=b^{5}(3b^5+1)(3b^5-1)\)
8. \(-2b^{7}+50b^{5}=-2b^{5}(b^2-25)=-2b^{5}(b-5)(b+5)\)
9. \(-18q^{7}+98q^{5}=-2q^{5}(9q^{2}-49)=-2q^{5}(3q+7)(3q-7)\)
10. \(50b^{6}-18b^{4}=2b^{4}(25b^{2}-9)=2b^{4}(5b+3)(5b-3)\)
11. \(-294a^{10}+504a^{7}s-216a^{4}s^2=-6a^{4}(49a^{6}-84a^3s+36s^2)=-6a^{4}(7a^3-6s)^2\)
12. \(98x^{5}+224x^{4}+128x^{3}=2x^{3}(49x^{2}+112x+64)=2x^{3}(7x+8)^2\)