Ontbinden in factoren (2)

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

1. \(3s^{4}+36s^{3}+108s^{2}\)
2. \(-2y^{6}+98y^{4}\)
3. \(-4x^{5}-4x^{4}-x^{3}\)
4. \(-a^{6}+9a^{4}\)
5. \(128a^{7}+32a^{5}q+2a^{3}q^2\)
6. \(320q^{7}+80q^{5}y+5q^{3}y^2\)
7. \(192s^{12}-336s^{7}+147s^{2}\)
8. \(-6p^{4}-84p^{3}-294p^{2}\)
9. \(-72s^{8}-24s^{5}x-2s^{2}x^2\)
10. \(-50x^{4}+2x^{2}\)
11. \(-5s^{7}+60s^{6}-180s^{5}\)
12. \(16x^{8}-24x^{6}+9x^{4}\)

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

Verbetersleutel

1. \(3s^{4}+36s^{3}+108s^{2}=3s^{2}(s^2+12s+36)=3s^{2}(s+6)^2\)
2. \(-2y^{6}+98y^{4}=-2y^{4}(y^2-49)=-2y^{4}(y-7)(y+7)\)
3. \(-4x^{5}-4x^{4}-x^{3}=-x^{3}(4x^{2}+4x+1)=-x^{3}(2x+1)^2\)
4. \(-a^{6}+9a^{4}=-a^{4}(a^2-9)=-a^{4}(a-3)(a+3)\)
5. \(128a^{7}+32a^{5}q+2a^{3}q^2=2a^{3}(64a^{4}+16a^2q+q^2)=2a^{3}(8a^2+q)^2\)
6. \(320q^{7}+80q^{5}y+5q^{3}y^2=5q^{3}(64q^{4}+16q^2y+y^2)=5q^{3}(8q^2+y)^2\)
7. \(192s^{12}-336s^{7}+147s^{2}=3s^{2}(64s^{10}-112s^5+49)=3s^{2}(8s^5-7)^2\)
8. \(-6p^{4}-84p^{3}-294p^{2}=-6p^{2}(p^2+14p+49)=-6p^{2}(p+7)^2\)
9. \(-72s^{8}-24s^{5}x-2s^{2}x^2=-2s^{2}(36s^{6}+12s^3x+x^2)=-2s^{2}(6s^3+x)^2\)
10. \(-50x^{4}+2x^{2}=-2x^{2}(25x^{2}-1)=-2x^{2}(5x+1)(5x-1)\)
11. \(-5s^{7}+60s^{6}-180s^{5}=-5s^{5}(s^2-12s+36)=-5s^{5}(s-6)^2\)
12. \(16x^{8}-24x^{6}+9x^{4}=x^{4}(16x^{4}-24x^2+9)=x^{4}(4x^2-3)^2\)