Ontbinden in factoren (2)

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

1. \(-128b^{12}+160b^{7}-50b^{2}\)
2. \(147s^{14}+84s^{9}x+12s^{4}x^2\)
3. \(-3q^{4}-24q^{3}-48q^{2}\)
4. \(320a^{6}+240a^{5}+45a^{4}\)
5. \(3y^{5}+12y^{4}+12y^{3}\)
6. \(108q^{6}-75q^{4}\)
7. \(-9p^{10}+49p^{2}\)
8. \(3s^{6}-3s^{4}\)
9. \(25s^{7}-49s^{5}\)
10. \(-6x^{5}-72x^{4}-216x^{3}\)
11. \(-54a^{4}-252a^{3}-294a^{2}\)
12. \(108a^{4}-3a^{2}\)

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

Verbetersleutel

1. \(-128b^{12}+160b^{7}-50b^{2}=-2b^{2}(64b^{10}-80b^5+25)=-2b^{2}(8b^5-5)^2\)
2. \(147s^{14}+84s^{9}x+12s^{4}x^2=3s^{4}(49s^{10}+28s^5x+4x^2)=3s^{4}(7s^5+2x)^2\)
3. \(-3q^{4}-24q^{3}-48q^{2}=-3q^{2}(q^2+8q+16)=-3q^{2}(q+4)^2\)
4. \(320a^{6}+240a^{5}+45a^{4}=5a^{4}(64a^{2}+48a+9)=5a^{4}(8a+3)^2\)
5. \(3y^{5}+12y^{4}+12y^{3}=3y^{3}(y^2+4y+4)=3y^{3}(y+2)^2\)
6. \(108q^{6}-75q^{4}=3q^{4}(36q^{2}-25)=3q^{4}(6q+5)(6q-5)\)
7. \(-9p^{10}+49p^{2}=-p^{2}(9p^{8}-49)=-p^{2}(3p^4+7)(3p^4-7)\)
8. \(3s^{6}-3s^{4}=3s^{4}(s^2-1)=3s^{4}(s+1)(s-1)\)
9. \(25s^{7}-49s^{5}=s^{5}(25s^{2}-49)=s^{5}(5s+7)(5s-7)\)
10. \(-6x^{5}-72x^{4}-216x^{3}=-6x^{3}(x^2+12x+36)=-6x^{3}(x+6)^2\)
11. \(-54a^{4}-252a^{3}-294a^{2}=-6a^{2}(9a^{2}+42a+49)=-6a^{2}(3a+7)^2\)
12. \(108a^{4}-3a^{2}=3a^{2}(36a^{2}-1)=3a^{2}(6a+1)(6a-1)\)