Ontbinden in factoren (2)

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

1. \(s^{4}+2s^{3}+s^{2}\)
2. \(-150y^{7}+6y^{5}\)
3. \(6p^{5}+36p^{4}+54p^{3}\)
4. \(36x^{5}-25x^{3}\)
5. \(-6q^{5}-12q^{4}-6q^{3}\)
6. \(-20b^{5}+245b^{3}\)
7. \(3s^{4}+24s^{3}+48s^{2}\)
8. \(-50q^{4}+18q^{2}\)
9. \(32s^{11}-50s^{3}\)
10. \(150b^{14}+60b^{9}y+6b^{4}y^2\)
11. \(-180q^{6}+125q^{2}\)
12. \(-12x^{10}-12x^{7}-3x^{4}\)

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

Verbetersleutel

1. \(s^{4}+2s^{3}+s^{2}=s^{2}(s^2+2s+1)=s^{2}(s+1)^2\)
2. \(-150y^{7}+6y^{5}=-6y^{5}(25y^{2}-1)=-6y^{5}(5y+1)(5y-1)\)
3. \(6p^{5}+36p^{4}+54p^{3}=6p^{3}(p^2+6p+9)=6p^{3}(p+3)^2\)
4. \(36x^{5}-25x^{3}=x^{3}(36x^{2}-25)=x^{3}(6x+5)(6x-5)\)
5. \(-6q^{5}-12q^{4}-6q^{3}=-6q^{3}(q^2+2q+1)=-6q^{3}(q+1)^2\)
6. \(-20b^{5}+245b^{3}=-5b^{3}(4b^{2}-49)=-5b^{3}(2b+7)(2b-7)\)
7. \(3s^{4}+24s^{3}+48s^{2}=3s^{2}(s^2+8s+16)=3s^{2}(s+4)^2\)
8. \(-50q^{4}+18q^{2}=-2q^{2}(25q^{2}-9)=-2q^{2}(5q+3)(5q-3)\)
9. \(32s^{11}-50s^{3}=2s^{3}(16s^{8}-25)=2s^{3}(4s^4+5)(4s^4-5)\)
10. \(150b^{14}+60b^{9}y+6b^{4}y^2=6b^{4}(25b^{10}+10b^5y+y^2)=6b^{4}(5b^5+y)^2\)
11. \(-180q^{6}+125q^{2}=-5q^{2}(36q^{4}-25)=-5q^{2}(6q^2+5)(6q^2-5)\)
12. \(-12x^{10}-12x^{7}-3x^{4}=-3x^{4}(4x^{6}+4x^3+1)=-3x^{4}(2x^3+1)^2\)