Ontbinden in factoren (2)

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

1. \(-3s^{4}+42s^{3}-147s^{2}\)
2. \(-4a^{4}+9a^{2}\)
3. \(-5p^{4}+20p^{2}\)
4. \(6a^{4}-36a^{3}+54a^{2}\)
5. \(6q^{4}-6q^{2}\)
6. \(4q^{11}+4q^{8}+q^{5}\)
7. \(128q^{10}-224q^{6}+98q^{2}\)
8. \(45p^{10}-125p^{2}\)
9. \(-24x^{6}-24x^{4}-6x^{2}\)
10. \(-8b^{4}+50b^{2}\)
11. \(12y^{13}+12y^{8}+3y^{3}\)
12. \(-4y^{15}-4y^{10}-y^{5}\)

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

Verbetersleutel

1. \(-3s^{4}+42s^{3}-147s^{2}=-3s^{2}(s^2-14s+49)=-3s^{2}(s-7)^2\)
2. \(-4a^{4}+9a^{2}=-a^{2}(4a^{2}-9)=-a^{2}(2a+3)(2a-3)\)
3. \(-5p^{4}+20p^{2}=-5p^{2}(p^2-4)=-5p^{2}(p-2)(p+2)\)
4. \(6a^{4}-36a^{3}+54a^{2}=6a^{2}(a^2-6a+9)=6a^{2}(a-3)^2\)
5. \(6q^{4}-6q^{2}=6q^{2}(q^2-1)=6q^{2}(q+1)(q-1)\)
6. \(4q^{11}+4q^{8}+q^{5}=q^{5}(4q^{6}+4q^3+1)=q^{5}(2q^3+1)^2\)
7. \(128q^{10}-224q^{6}+98q^{2}=2q^{2}(64q^{8}-112q^4+49)=2q^{2}(8q^4-7)^2\)
8. \(45p^{10}-125p^{2}=5p^{2}(9p^{8}-25)=5p^{2}(3p^4+5)(3p^4-5)\)
9. \(-24x^{6}-24x^{4}-6x^{2}=-6x^{2}(4x^{4}+4x^2+1)=-6x^{2}(2x^2+1)^2\)
10. \(-8b^{4}+50b^{2}=-2b^{2}(4b^{2}-25)=-2b^{2}(2b+5)(2b-5)\)
11. \(12y^{13}+12y^{8}+3y^{3}=3y^{3}(4y^{10}+4y^5+1)=3y^{3}(2y^5+1)^2\)
12. \(-4y^{15}-4y^{10}-y^{5}=-y^{5}(4y^{10}+4y^5+1)=-y^{5}(2y^5+1)^2\)