Ontbinden in factoren (2)

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

1. \(-50b^{12}+140b^{7}-98b^{2}\)
2. \(6s^{7}-96s^{6}+384s^{5}\)
3. \(-3b^{7}+12b^{5}\)
4. \(-150q^{6}+54q^{2}\)
5. \(-27p^{6}+147p^{4}\)
6. \(-80s^{5}+280s^{4}-245s^{3}\)
7. \(-6a^{6}+294a^{4}\)
8. \(20q^{7}-45q^{5}\)
9. \(45s^{6}-60s^{5}+20s^{4}\)
10. \(-18s^{14}+8s^{2}\)
11. \(32a^{7}+48a^{6}+18a^{5}\)
12. \(-3a^{6}+42a^{5}-147a^{4}\)

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

Verbetersleutel

1. \(-50b^{12}+140b^{7}-98b^{2}=-2b^{2}(25b^{10}-70b^5+49)=-2b^{2}(5b^5-7)^2\)
2. \(6s^{7}-96s^{6}+384s^{5}=6s^{5}(s^2-16s+64)=6s^{5}(s-8)^2\)
3. \(-3b^{7}+12b^{5}=-3b^{5}(b^2-4)=-3b^{5}(b-2)(b+2)\)
4. \(-150q^{6}+54q^{2}=-6q^{2}(25q^{4}-9)=-6q^{2}(5q^2+3)(5q^2-3)\)
5. \(-27p^{6}+147p^{4}=-3p^{4}(9p^{2}-49)=-3p^{4}(3p+7)(3p-7)\)
6. \(-80s^{5}+280s^{4}-245s^{3}=-5s^{3}(16s^{2}-56s+49)=-5s^{3}(4s-7)^2\)
7. \(-6a^{6}+294a^{4}=-6a^{4}(a^2-49)=-6a^{4}(a-7)(a+7)\)
8. \(20q^{7}-45q^{5}=5q^{5}(4q^{2}-9)=5q^{5}(2q+3)(2q-3)\)
9. \(45s^{6}-60s^{5}+20s^{4}=5s^{4}(9s^{2}-12s+4)=5s^{4}(3s-2)^2\)
10. \(-18s^{14}+8s^{2}=-2s^{2}(9s^{12}-4)=-2s^{2}(3s^6+2)(3s^6-2)\)
11. \(32a^{7}+48a^{6}+18a^{5}=2a^{5}(16a^{2}+24a+9)=2a^{5}(4a+3)^2\)
12. \(-3a^{6}+42a^{5}-147a^{4}=-3a^{4}(a^2-14a+49)=-3a^{4}(a-7)^2\)