Ontbinden in factoren (2)

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

1. \(-27x^{14}+75x^{2}\)
2. \(-108p^{5}-36p^{4}-3p^{3}\)
3. \(-6q^{5}+216q^{3}\)
4. \(-2s^{4}+8s^{2}\)
5. \(-36p^{16}+25p^{4}\)
6. \(-294p^{9}-336p^{7}q-96p^{5}q^2\)
7. \(-24s^{13}-72s^{8}-54s^{3}\)
8. \(p^{4}+12p^{3}+36p^{2}\)
9. \(q^{6}-6q^{5}+9q^{4}\)
10. \(-12y^{4}+147y^{2}\)
11. \(-5s^{5}+10s^{4}-5s^{3}\)
12. \(64x^{5}-112x^{4}+49x^{3}\)

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

Verbetersleutel

1. \(-27x^{14}+75x^{2}=-3x^{2}(9x^{12}-25)=-3x^{2}(3x^6+5)(3x^6-5)\)
2. \(-108p^{5}-36p^{4}-3p^{3}=-3p^{3}(36p^{2}+12p+1)=-3p^{3}(6p+1)^2\)
3. \(-6q^{5}+216q^{3}=-6q^{3}(q^2-36)=-6q^{3}(q+6)(q-6)\)
4. \(-2s^{4}+8s^{2}=-2s^{2}(s^2-4)=-2s^{2}(s-2)(s+2)\)
5. \(-36p^{16}+25p^{4}=-p^{4}(36p^{12}-25)=-p^{4}(6p^6+5)(6p^6-5)\)
6. \(-294p^{9}-336p^{7}q-96p^{5}q^2=-6p^{5}(49p^{4}+56p^2q+16q^2)=-6p^{5}(7p^2+4q)^2\)
7. \(-24s^{13}-72s^{8}-54s^{3}=-6s^{3}(4s^{10}+12s^5+9)=-6s^{3}(2s^5+3)^2\)
8. \(p^{4}+12p^{3}+36p^{2}=p^{2}(p^2+12p+36)=p^{2}(p+6)^2\)
9. \(q^{6}-6q^{5}+9q^{4}=q^{4}(q^2-6q+9)=q^{4}(q-3)^2\)
10. \(-12y^{4}+147y^{2}=-3y^{2}(4y^{2}-49)=-3y^{2}(2y+7)(2y-7)\)
11. \(-5s^{5}+10s^{4}-5s^{3}=-5s^{3}(s^2-2s+1)=-5s^{3}(s-1)^2\)
12. \(64x^{5}-112x^{4}+49x^{3}=x^{3}(64x^{2}-112x+49)=x^{3}(8x-7)^2\)