Ontbinden in factoren (2)

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

1. \(-75s^{4}+60s^{3}-12s^{2}\)
2. \(-6p^{4}+48p^{3}-96p^{2}\)
3. \(2b^{7}-28b^{6}+98b^{5}\)
4. \(12q^{6}-27q^{4}\)
5. \(24s^{8}+24s^{5}+6s^{2}\)
6. \(16q^{8}+8q^{5}+q^{2}\)
7. \(12q^{8}-147q^{2}\)
8. \(36s^{7}-25s^{5}\)
9. \(-180b^{5}+300b^{4}-125b^{3}\)
10. \(-a^{4}+64a^{2}\)
11. \(5y^{4}+70y^{3}+245y^{2}\)
12. \(216b^{21}-294b^{5}\)

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

Verbetersleutel

1. \(-75s^{4}+60s^{3}-12s^{2}=-3s^{2}(25s^{2}-20s+4)=-3s^{2}(5s-2)^2\)
2. \(-6p^{4}+48p^{3}-96p^{2}=-6p^{2}(p^2-8p+16)=-6p^{2}(p-4)^2\)
3. \(2b^{7}-28b^{6}+98b^{5}=2b^{5}(b^2-14b+49)=2b^{5}(b-7)^2\)
4. \(12q^{6}-27q^{4}=3q^{4}(4q^{2}-9)=3q^{4}(2q+3)(2q-3)\)
5. \(24s^{8}+24s^{5}+6s^{2}=6s^{2}(4s^{6}+4s^3+1)=6s^{2}(2s^3+1)^2\)
6. \(16q^{8}+8q^{5}+q^{2}=q^{2}(16q^{6}+8q^3+1)=q^{2}(4q^3+1)^2\)
7. \(12q^{8}-147q^{2}=3q^{2}(4q^{6}-49)=3q^{2}(2q^3+7)(2q^3-7)\)
8. \(36s^{7}-25s^{5}=s^{5}(36s^{2}-25)=s^{5}(6s+5)(6s-5)\)
9. \(-180b^{5}+300b^{4}-125b^{3}=-5b^{3}(36b^{2}-60b+25)=-5b^{3}(6b-5)^2\)
10. \(-a^{4}+64a^{2}=-a^{2}(a^2-64)=-a^{2}(a-8)(a+8)\)
11. \(5y^{4}+70y^{3}+245y^{2}=5y^{2}(y^2+14y+49)=5y^{2}(y+7)^2\)
12. \(216b^{21}-294b^{5}=6b^{5}(36b^{16}-49)=6b^{5}(6b^8+7)(6b^8-7)\)