Ontbinden in factoren (2)

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

1. \(3p^{6}-147p^{4}\)
2. \(4p^{10}-p^{4}\)
3. \(-4s^{9}-4s^{7}x-s^{5}x^2\)
4. \(3s^{6}-75s^{4}\)
5. \(32q^{7}+112q^{6}+98q^{5}\)
6. \(-2q^{7}+8q^{5}\)
7. \(-8p^{18}+50p^{2}\)
8. \(p^{5}-p^{3}\)
9. \(192y^{12}+144y^{7}+27y^{2}\)
10. \(2x^{7}-50x^{5}\)
11. \(150y^{4}-120y^{3}+24y^{2}\)
12. \(-48p^{6}+3p^{4}\)

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

Verbetersleutel

1. \(3p^{6}-147p^{4}=3p^{4}(p^2-49)=3p^{4}(p-7)(p+7)\)
2. \(4p^{10}-p^{4}=p^{4}(4p^{6}-1)=p^{4}(2p^3+1)(2p^3-1)\)
3. \(-4s^{9}-4s^{7}x-s^{5}x^2=-s^{5}(4s^{4}+4s^2x+x^2)=-s^{5}(2s^2+x)^2\)
4. \(3s^{6}-75s^{4}=3s^{4}(s^2-25)=3s^{4}(s+5)(s-5)\)
5. \(32q^{7}+112q^{6}+98q^{5}=2q^{5}(16q^{2}+56q+49)=2q^{5}(4q+7)^2\)
6. \(-2q^{7}+8q^{5}=-2q^{5}(q^2-4)=-2q^{5}(q-2)(q+2)\)
7. \(-8p^{18}+50p^{2}=-2p^{2}(4p^{16}-25)=-2p^{2}(2p^8+5)(2p^8-5)\)
8. \(p^{5}-p^{3}=p^{3}(p^2-1)=p^{3}(p-1)(p+1)\)
9. \(192y^{12}+144y^{7}+27y^{2}=3y^{2}(64y^{10}+48y^5+9)=3y^{2}(8y^5+3)^2\)
10. \(2x^{7}-50x^{5}=2x^{5}(x^2-25)=2x^{5}(x+5)(x-5)\)
11. \(150y^{4}-120y^{3}+24y^{2}=6y^{2}(25y^{2}-20y+4)=6y^{2}(5y-2)^2\)
12. \(-48p^{6}+3p^{4}=-3p^{4}(16p^{2}-1)=-3p^{4}(4p+1)(4p-1)\)