Ontbinden in factoren (2)

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

1. \(-108s^{7}+180s^{6}-75s^{5}\)
2. \(32x^{19}-18x^{5}\)
3. \(-q^{4}+8q^{3}-16q^{2}\)
4. \(-45q^{6}+245q^{4}\)
5. \(5a^{4}-125a^{2}\)
6. \(-150x^{6}+216x^{4}\)
7. \(192x^{6}-336x^{5}+147x^{4}\)
8. \(6p^{4}-24p^{2}\)
9. \(-2s^{4}+18s^{2}\)
10. \(-18y^{8}+60y^{6}-50y^{4}\)
11. \(98q^{7}-84q^{5}y+18q^{3}y^2\)
12. \(27q^{12}+90q^{7}+75q^{2}\)

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

Verbetersleutel

1. \(-108s^{7}+180s^{6}-75s^{5}=-3s^{5}(36s^{2}-60s+25)=-3s^{5}(6s-5)^2\)
2. \(32x^{19}-18x^{5}=2x^{5}(16x^{14}-9)=2x^{5}(4x^7+3)(4x^7-3)\)
3. \(-q^{4}+8q^{3}-16q^{2}=-q^{2}(q^2-8q+16)=-q^{2}(q-4)^2\)
4. \(-45q^{6}+245q^{4}=-5q^{4}(9q^{2}-49)=-5q^{4}(3q+7)(3q-7)\)
5. \(5a^{4}-125a^{2}=5a^{2}(a^2-25)=5a^{2}(a-5)(a+5)\)
6. \(-150x^{6}+216x^{4}=-6x^{4}(25x^{2}-36)=-6x^{4}(5x+6)(5x-6)\)
7. \(192x^{6}-336x^{5}+147x^{4}=3x^{4}(64x^{2}-112x+49)=3x^{4}(8x-7)^2\)
8. \(6p^{4}-24p^{2}=6p^{2}(p^2-4)=6p^{2}(p-2)(p+2)\)
9. \(-2s^{4}+18s^{2}=-2s^{2}(s^2-9)=-2s^{2}(s-3)(s+3)\)
10. \(-18y^{8}+60y^{6}-50y^{4}=-2y^{4}(9y^{4}-30y^2+25)=-2y^{4}(3y^2-5)^2\)
11. \(98q^{7}-84q^{5}y+18q^{3}y^2=2q^{3}(49q^{4}-42q^2y+9y^2)=2q^{3}(7q^2-3y)^2\)
12. \(27q^{12}+90q^{7}+75q^{2}=3q^{2}(9q^{10}+30q^5+25)=3q^{2}(3q^5+5)^2\)