Ontbinden in factoren (2)

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

1. \(48x^{14}-3x^{2}\)
2. \(8q^{13}+8q^{9}s+2q^{5}s^2\)
3. \(-12x^{5}+147x^{3}\)
4. \(-150s^{6}+6s^{2}\)
5. \(-48p^{7}+75p^{5}\)
6. \(24a^{9}+24a^{6}x+6a^{3}x^2\)
7. \(-216a^{8}+360a^{6}-150a^{4}\)
8. \(-3a^{6}+147a^{4}\)
9. \(125y^{8}-200y^{5}+80y^{2}\)
10. \(-4x^{15}-4x^{10}y-x^{5}y^2\)
11. \(5y^{4}+30y^{3}+45y^{2}\)
12. \(96b^{6}-144b^{4}s+54b^{2}s^2\)

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

Verbetersleutel

1. \(48x^{14}-3x^{2}=3x^{2}(16x^{12}-1)=3x^{2}(4x^6+1)(4x^6-1)\)
2. \(8q^{13}+8q^{9}s+2q^{5}s^2=2q^{5}(4q^{8}+4q^4s+s^2)=2q^{5}(2q^4+s)^2\)
3. \(-12x^{5}+147x^{3}=-3x^{3}(4x^{2}-49)=-3x^{3}(2x+7)(2x-7)\)
4. \(-150s^{6}+6s^{2}=-6s^{2}(25s^{4}-1)=-6s^{2}(5s^2+1)(5s^2-1)\)
5. \(-48p^{7}+75p^{5}=-3p^{5}(16p^{2}-25)=-3p^{5}(4p+5)(4p-5)\)
6. \(24a^{9}+24a^{6}x+6a^{3}x^2=6a^{3}(4a^{6}+4a^3x+x^2)=6a^{3}(2a^3+x)^2\)
7. \(-216a^{8}+360a^{6}-150a^{4}=-6a^{4}(36a^{4}-60a^2+25)=-6a^{4}(6a^2-5)^2\)
8. \(-3a^{6}+147a^{4}=-3a^{4}(a^2-49)=-3a^{4}(a+7)(a-7)\)
9. \(125y^{8}-200y^{5}+80y^{2}=5y^{2}(25y^{6}-40y^3+16)=5y^{2}(5y^3-4)^2\)
10. \(-4x^{15}-4x^{10}y-x^{5}y^2=-x^{5}(4x^{10}+4x^5y+y^2)=-x^{5}(2x^5+y)^2\)
11. \(5y^{4}+30y^{3}+45y^{2}=5y^{2}(y^2+6y+9)=5y^{2}(y+3)^2\)
12. \(96b^{6}-144b^{4}s+54b^{2}s^2=6b^{2}(16b^{4}-24b^2s+9s^2)=6b^{2}(4b^2-3s)^2\)