Ontbinden in factoren (2)

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

1. \(98s^{11}-56s^{8}x+8s^{5}x^2\)
2. \(2a^{4}-20a^{3}+50a^{2}\)
3. \(2s^{6}+20s^{5}+50s^{4}\)
4. \(-192s^{12}-48s^{8}x-3s^{4}x^2\)
5. \(384b^{10}-672b^{6}+294b^{2}\)
6. \(216x^{4}-150x^{2}\)
7. \(25p^{10}-16p^{4}\)
8. \(-216s^{8}+6s^{2}\)
9. \(5q^{7}-5q^{5}\)
10. \(32b^{18}-50b^{2}\)
11. \(108p^{7}+180p^{6}+75p^{5}\)
12. \(5p^{6}-70p^{5}+245p^{4}\)

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

Verbetersleutel

1. \(98s^{11}-56s^{8}x+8s^{5}x^2=2s^{5}(49s^{6}-28s^3x+4x^2)=2s^{5}(7s^3-2x)^2\)
2. \(2a^{4}-20a^{3}+50a^{2}=2a^{2}(a^2-10a+25)=2a^{2}(a-5)^2\)
3. \(2s^{6}+20s^{5}+50s^{4}=2s^{4}(s^2+10s+25)=2s^{4}(s+5)^2\)
4. \(-192s^{12}-48s^{8}x-3s^{4}x^2=-3s^{4}(64s^{8}+16s^4x+x^2)=-3s^{4}(8s^4+x)^2\)
5. \(384b^{10}-672b^{6}+294b^{2}=6b^{2}(64b^{8}-112b^4+49)=6b^{2}(8b^4-7)^2\)
6. \(216x^{4}-150x^{2}=6x^{2}(36x^{2}-25)=6x^{2}(6x+5)(6x-5)\)
7. \(25p^{10}-16p^{4}=p^{4}(25p^{6}-16)=p^{4}(5p^3+4)(5p^3-4)\)
8. \(-216s^{8}+6s^{2}=-6s^{2}(36s^{6}-1)=-6s^{2}(6s^3+1)(6s^3-1)\)
9. \(5q^{7}-5q^{5}=5q^{5}(q^2-1)=5q^{5}(q+1)(q-1)\)
10. \(32b^{18}-50b^{2}=2b^{2}(16b^{16}-25)=2b^{2}(4b^8+5)(4b^8-5)\)
11. \(108p^{7}+180p^{6}+75p^{5}=3p^{5}(36p^{2}+60p+25)=3p^{5}(6p+5)^2\)
12. \(5p^{6}-70p^{5}+245p^{4}=5p^{4}(p^2-14p+49)=5p^{4}(p-7)^2\)