Ontbinden in factoren (2)

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

1. \(-20p^{5}-60p^{4}-45p^{3}\)
2. \(-384p^{8}+672p^{6}q-294p^{4}q^2\)
3. \(-216q^{8}-360q^{5}-150q^{2}\)
4. \(-48q^{7}-24q^{6}-3q^{5}\)
5. \(24q^{5}-150q^{3}\)
6. \(2x^{5}-16x^{4}+32x^{3}\)
7. \(5p^{4}-80p^{2}\)
8. \(-6b^{5}+384b^{3}\)
9. \(-3s^{7}-12s^{6}-12s^{5}\)
10. \(3x^{7}+54x^{6}+243x^{5}\)
11. \(2b^{5}-32b^{3}\)
12. \(6y^{4}-24y^{2}\)

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

Verbetersleutel

1. \(-20p^{5}-60p^{4}-45p^{3}=-5p^{3}(4p^{2}+12p+9)=-5p^{3}(2p+3)^2\)
2. \(-384p^{8}+672p^{6}q-294p^{4}q^2=-6p^{4}(64p^{4}-112p^2q+49q^2)=-6p^{4}(8p^2-7q)^2\)
3. \(-216q^{8}-360q^{5}-150q^{2}=-6q^{2}(36q^{6}+60q^3+25)=-6q^{2}(6q^3+5)^2\)
4. \(-48q^{7}-24q^{6}-3q^{5}=-3q^{5}(16q^{2}+8q+1)=-3q^{5}(4q+1)^2\)
5. \(24q^{5}-150q^{3}=6q^{3}(4q^{2}-25)=6q^{3}(2q+5)(2q-5)\)
6. \(2x^{5}-16x^{4}+32x^{3}=2x^{3}(x^2-8x+16)=2x^{3}(x-4)^2\)
7. \(5p^{4}-80p^{2}=5p^{2}(p^2-16)=5p^{2}(p+4)(p-4)\)
8. \(-6b^{5}+384b^{3}=-6b^{3}(b^2-64)=-6b^{3}(b-8)(b+8)\)
9. \(-3s^{7}-12s^{6}-12s^{5}=-3s^{5}(s^2+4s+4)=-3s^{5}(s+2)^2\)
10. \(3x^{7}+54x^{6}+243x^{5}=3x^{5}(x^2+18x+81)=3x^{5}(x+9)^2\)
11. \(2b^{5}-32b^{3}=2b^{3}(b^2-16)=2b^{3}(b+4)(b-4)\)
12. \(6y^{4}-24y^{2}=6y^{2}(y^2-4)=6y^{2}(y+2)(y-2)\)