Ontbinden in factoren (2)

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

1. \(25s^{12}+10s^{7}+s^{2}\)
2. \(3s^{5}-36s^{4}+108s^{3}\)
3. \(-150b^{6}+216b^{4}\)
4. \(-80a^{19}+5a^{3}\)
5. \(2s^{7}-128s^{5}\)
6. \(25a^{11}+60a^{8}x+36a^{5}x^2\)
7. \(5p^{7}-5p^{5}\)
8. \(64q^{8}-112q^{5}s+49q^{2}s^2\)
9. \(50a^{14}-40a^{9}p+8a^{4}p^2\)
10. \(3s^{6}-75s^{4}\)
11. \(-75a^{14}-180a^{9}b-108a^{4}b^2\)
12. \(-5q^{6}+20q^{4}\)

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

Verbetersleutel

1. \(25s^{12}+10s^{7}+s^{2}=s^{2}(25s^{10}+10s^5+1)=s^{2}(5s^5+1)^2\)
2. \(3s^{5}-36s^{4}+108s^{3}=3s^{3}(s^2-12s+36)=3s^{3}(s-6)^2\)
3. \(-150b^{6}+216b^{4}=-6b^{4}(25b^{2}-36)=-6b^{4}(5b+6)(5b-6)\)
4. \(-80a^{19}+5a^{3}=-5a^{3}(16a^{16}-1)=-5a^{3}(4a^8+1)(4a^8-1)\)
5. \(2s^{7}-128s^{5}=2s^{5}(s^2-64)=2s^{5}(s+8)(s-8)\)
6. \(25a^{11}+60a^{8}x+36a^{5}x^2=a^{5}(25a^{6}+60a^3x+36x^2)=a^{5}(5a^3+6x)^2\)
7. \(5p^{7}-5p^{5}=5p^{5}(p^2-1)=5p^{5}(p-1)(p+1)\)
8. \(64q^{8}-112q^{5}s+49q^{2}s^2=q^{2}(64q^{6}-112q^3s+49s^2)=q^{2}(8q^3-7s)^2\)
9. \(50a^{14}-40a^{9}p+8a^{4}p^2=2a^{4}(25a^{10}-20a^5p+4p^2)=2a^{4}(5a^5-2p)^2\)
10. \(3s^{6}-75s^{4}=3s^{4}(s^2-25)=3s^{4}(s+5)(s-5)\)
11. \(-75a^{14}-180a^{9}b-108a^{4}b^2=-3a^{4}(25a^{10}+60a^5b+36b^2)=-3a^{4}(5a^5+6b)^2\)
12. \(-5q^{6}+20q^{4}=-5q^{4}(q^2-4)=-5q^{4}(q-2)(q+2)\)