Ontbinden in factoren (2)

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

1. \(-320s^{9}+560s^{7}x-245s^{5}x^2\)
2. \(-192q^{4}+240q^{3}-75q^{2}\)
3. \(216y^{6}-150y^{4}\)
4. \(-6a^{4}+54a^{2}\)
5. \(125b^{15}+50b^{10}+5b^{5}\)
6. \(50a^{12}+80a^{7}x+32a^{2}x^2\)
7. \(25x^{13}-36x^{3}\)
8. \(-36x^{7}+60x^{6}-25x^{5}\)
9. \(-245x^{7}-420x^{5}y-180x^{3}y^2\)
10. \(3b^{5}-192b^{3}\)
11. \(45q^{9}+60q^{7}s+20q^{5}s^2\)
12. \(-147b^{9}-42b^{6}-3b^{3}\)

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

Verbetersleutel

1. \(-320s^{9}+560s^{7}x-245s^{5}x^2=-5s^{5}(64s^{4}-112s^2x+49x^2)=-5s^{5}(8s^2-7x)^2\)
2. \(-192q^{4}+240q^{3}-75q^{2}=-3q^{2}(64q^{2}-80q+25)=-3q^{2}(8q-5)^2\)
3. \(216y^{6}-150y^{4}=6y^{4}(36y^{2}-25)=6y^{4}(6y+5)(6y-5)\)
4. \(-6a^{4}+54a^{2}=-6a^{2}(a^2-9)=-6a^{2}(a-3)(a+3)\)
5. \(125b^{15}+50b^{10}+5b^{5}=5b^{5}(25b^{10}+10b^5+1)=5b^{5}(5b^5+1)^2\)
6. \(50a^{12}+80a^{7}x+32a^{2}x^2=2a^{2}(25a^{10}+40a^5x+16x^2)=2a^{2}(5a^5+4x)^2\)
7. \(25x^{13}-36x^{3}=x^{3}(25x^{10}-36)=x^{3}(5x^5+6)(5x^5-6)\)
8. \(-36x^{7}+60x^{6}-25x^{5}=-x^{5}(36x^{2}-60x+25)=-x^{5}(6x-5)^2\)
9. \(-245x^{7}-420x^{5}y-180x^{3}y^2=-5x^{3}(49x^{4}+84x^2y+36y^2)=-5x^{3}(7x^2+6y)^2\)
10. \(3b^{5}-192b^{3}=3b^{3}(b^2-64)=3b^{3}(b-8)(b+8)\)
11. \(45q^{9}+60q^{7}s+20q^{5}s^2=5q^{5}(9q^{4}+12q^2s+4s^2)=5q^{5}(3q^2+2s)^2\)
12. \(-147b^{9}-42b^{6}-3b^{3}=-3b^{3}(49b^{6}+14b^3+1)=-3b^{3}(7b^3+1)^2\)