Ontbinden in factoren (2)

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

1. \(50x^{4}-8x^{2}\)
2. \(18x^{15}-2x^{3}\)
3. \(-80q^{5}+245q^{3}\)
4. \(-8p^{5}-8p^{4}-2p^{3}\)
5. \(-4a^{19}+a^{5}\)
6. \(-192x^{13}-48x^{9}-3x^{5}\)
7. \(-5s^{6}+10s^{5}-5s^{4}\)
8. \(-3x^{4}+48x^{2}\)
9. \(96p^{5}-6p^{3}\)
10. \(-6y^{4}+84y^{3}-294y^{2}\)
11. \(-2x^{4}+72x^{2}\)
12. \(-5s^{4}+320s^{2}\)

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

Verbetersleutel

1. \(50x^{4}-8x^{2}=2x^{2}(25x^{2}-4)=2x^{2}(5x+2)(5x-2)\)
2. \(18x^{15}-2x^{3}=2x^{3}(9x^{12}-1)=2x^{3}(3x^6+1)(3x^6-1)\)
3. \(-80q^{5}+245q^{3}=-5q^{3}(16q^{2}-49)=-5q^{3}(4q+7)(4q-7)\)
4. \(-8p^{5}-8p^{4}-2p^{3}=-2p^{3}(4p^{2}+4p+1)=-2p^{3}(2p+1)^2\)
5. \(-4a^{19}+a^{5}=-a^{5}(4a^{14}-1)=-a^{5}(2a^7+1)(2a^7-1)\)
6. \(-192x^{13}-48x^{9}-3x^{5}=-3x^{5}(64x^{8}+16x^4+1)=-3x^{5}(8x^4+1)^2\)
7. \(-5s^{6}+10s^{5}-5s^{4}=-5s^{4}(s^2-2s+1)=-5s^{4}(s-1)^2\)
8. \(-3x^{4}+48x^{2}=-3x^{2}(x^2-16)=-3x^{2}(x-4)(x+4)\)
9. \(96p^{5}-6p^{3}=6p^{3}(16p^{2}-1)=6p^{3}(4p+1)(4p-1)\)
10. \(-6y^{4}+84y^{3}-294y^{2}=-6y^{2}(y^2-14y+49)=-6y^{2}(y-7)^2\)
11. \(-2x^{4}+72x^{2}=-2x^{2}(x^2-36)=-2x^{2}(x+6)(x-6)\)
12. \(-5s^{4}+320s^{2}=-5s^{2}(s^2-64)=-5s^{2}(s-8)(s+8)\)