Ontbinden in factoren (2)

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

1. \(-216q^{15}-360q^{10}y-150q^{5}y^2\)
2. \(-50a^{8}+32a^{4}\)
3. \(147x^{8}+42x^{5}+3x^{2}\)
4. \(-36x^{5}+x^{3}\)
5. \(320p^{7}+80p^{6}+5p^{5}\)
6. \(-294s^{6}-84s^{5}-6s^{4}\)
7. \(294q^{12}+504q^{8}s+216q^{4}s^2\)
8. \(45p^{16}-245p^{4}\)
9. \(-5x^{6}+5x^{4}\)
10. \(54x^{16}-6x^{4}\)
11. \(-108p^{7}-252p^{6}-147p^{5}\)
12. \(-150a^{8}+240a^{6}x-96a^{4}x^2\)

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

Verbetersleutel

1. \(-216q^{15}-360q^{10}y-150q^{5}y^2=-6q^{5}(36q^{10}+60q^5y+25y^2)=-6q^{5}(6q^5+5y)^2\)
2. \(-50a^{8}+32a^{4}=-2a^{4}(25a^{4}-16)=-2a^{4}(5a^2+4)(5a^2-4)\)
3. \(147x^{8}+42x^{5}+3x^{2}=3x^{2}(49x^{6}+14x^3+1)=3x^{2}(7x^3+1)^2\)
4. \(-36x^{5}+x^{3}=-x^{3}(36x^{2}-1)=-x^{3}(6x+1)(6x-1)\)
5. \(320p^{7}+80p^{6}+5p^{5}=5p^{5}(64p^{2}+16p+1)=5p^{5}(8p+1)^2\)
6. \(-294s^{6}-84s^{5}-6s^{4}=-6s^{4}(49s^{2}+14s+1)=-6s^{4}(7s+1)^2\)
7. \(294q^{12}+504q^{8}s+216q^{4}s^2=6q^{4}(49q^{8}+84q^4s+36s^2)=6q^{4}(7q^4+6s)^2\)
8. \(45p^{16}-245p^{4}=5p^{4}(9p^{12}-49)=5p^{4}(3p^6+7)(3p^6-7)\)
9. \(-5x^{6}+5x^{4}=-5x^{4}(x^2-1)=-5x^{4}(x+1)(x-1)\)
10. \(54x^{16}-6x^{4}=6x^{4}(9x^{12}-1)=6x^{4}(3x^6+1)(3x^6-1)\)
11. \(-108p^{7}-252p^{6}-147p^{5}=-3p^{5}(36p^{2}+84p+49)=-3p^{5}(6p+7)^2\)
12. \(-150a^{8}+240a^{6}x-96a^{4}x^2=-6a^{4}(25a^{4}-40a^2x+16x^2)=-6a^{4}(5a^2-4x)^2\)