Ontbinden in factoren (2)

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

1. \(-6a^{7}+36a^{6}-54a^{5}\)
2. \(-150a^{11}+240a^{8}y-96a^{5}y^2\)
3. \(-294a^{11}-252a^{8}y-54a^{5}y^2\)
4. \(-5p^{4}+80p^{2}\)
5. \(5p^{5}-80p^{4}+320p^{3}\)
6. \(-54x^{6}-180x^{4}-150x^{2}\)
7. \(9a^{15}+6a^{10}x+a^{5}x^2\)
8. \(-6x^{4}+384x^{2}\)
9. \(-24x^{12}+6x^{2}\)
10. \(2q^{6}-18q^{4}\)
11. \(147p^{9}-126p^{7}s+27p^{5}s^2\)
12. \(s^{6}-25s^{4}\)

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

Verbetersleutel

1. \(-6a^{7}+36a^{6}-54a^{5}=-6a^{5}(a^2-6a+9)=-6a^{5}(a-3)^2\)
2. \(-150a^{11}+240a^{8}y-96a^{5}y^2=-6a^{5}(25a^{6}-40a^3y+16y^2)=-6a^{5}(5a^3-4y)^2\)
3. \(-294a^{11}-252a^{8}y-54a^{5}y^2=-6a^{5}(49a^{6}+42a^3y+9y^2)=-6a^{5}(7a^3+3y)^2\)
4. \(-5p^{4}+80p^{2}=-5p^{2}(p^2-16)=-5p^{2}(p+4)(p-4)\)
5. \(5p^{5}-80p^{4}+320p^{3}=5p^{3}(p^2-16p+64)=5p^{3}(p-8)^2\)
6. \(-54x^{6}-180x^{4}-150x^{2}=-6x^{2}(9x^{4}+30x^2+25)=-6x^{2}(3x^2+5)^2\)
7. \(9a^{15}+6a^{10}x+a^{5}x^2=a^{5}(9a^{10}+6a^5x+x^2)=a^{5}(3a^5+x)^2\)
8. \(-6x^{4}+384x^{2}=-6x^{2}(x^2-64)=-6x^{2}(x+8)(x-8)\)
9. \(-24x^{12}+6x^{2}=-6x^{2}(4x^{10}-1)=-6x^{2}(2x^5+1)(2x^5-1)\)
10. \(2q^{6}-18q^{4}=2q^{4}(q^2-9)=2q^{4}(q+3)(q-3)\)
11. \(147p^{9}-126p^{7}s+27p^{5}s^2=3p^{5}(49p^{4}-42p^2s+9s^2)=3p^{5}(7p^2-3s)^2\)
12. \(s^{6}-25s^{4}=s^{4}(s^2-25)=s^{4}(s+5)(s-5)\)