Ontbinden in factoren (2)

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

1. \(-6x^{4}-36x^{3}-54x^{2}\)
2. \(320b^{9}+80b^{7}q+5b^{5}q^2\)
3. \(8b^{7}+8b^{6}+2b^{5}\)
4. \(-12a^{8}-12a^{5}x-3a^{2}x^2\)
5. \(-8b^{6}-8b^{4}-2b^{2}\)
6. \(-3q^{5}-18q^{4}-27q^{3}\)
7. \(-3x^{7}+54x^{6}-243x^{5}\)
8. \(-3p^{4}+3p^{2}\)
9. \(20x^{4}-5x^{2}\)
10. \(54x^{6}-150x^{4}\)
11. \(-18q^{10}-24q^{7}-8q^{4}\)
12. \(48x^{10}+72x^{7}+27x^{4}\)

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

Verbetersleutel

1. \(-6x^{4}-36x^{3}-54x^{2}=-6x^{2}(x^2+6x+9)=-6x^{2}(x+3)^2\)
2. \(320b^{9}+80b^{7}q+5b^{5}q^2=5b^{5}(64b^{4}+16b^2q+q^2)=5b^{5}(8b^2+q)^2\)
3. \(8b^{7}+8b^{6}+2b^{5}=2b^{5}(4b^{2}+4b+1)=2b^{5}(2b+1)^2\)
4. \(-12a^{8}-12a^{5}x-3a^{2}x^2=-3a^{2}(4a^{6}+4a^3x+x^2)=-3a^{2}(2a^3+x)^2\)
5. \(-8b^{6}-8b^{4}-2b^{2}=-2b^{2}(4b^{4}+4b^2+1)=-2b^{2}(2b^2+1)^2\)
6. \(-3q^{5}-18q^{4}-27q^{3}=-3q^{3}(q^2+6q+9)=-3q^{3}(q+3)^2\)
7. \(-3x^{7}+54x^{6}-243x^{5}=-3x^{5}(x^2-18x+81)=-3x^{5}(x-9)^2\)
8. \(-3p^{4}+3p^{2}=-3p^{2}(p^2-1)=-3p^{2}(p-1)(p+1)\)
9. \(20x^{4}-5x^{2}=5x^{2}(4x^{2}-1)=5x^{2}(2x+1)(2x-1)\)
10. \(54x^{6}-150x^{4}=6x^{4}(9x^{2}-25)=6x^{4}(3x+5)(3x-5)\)
11. \(-18q^{10}-24q^{7}-8q^{4}=-2q^{4}(9q^{6}+12q^3+4)=-2q^{4}(3q^3+2)^2\)
12. \(48x^{10}+72x^{7}+27x^{4}=3x^{4}(16x^{6}+24x^3+9)=3x^{4}(4x^3+3)^2\)