Ontbinden in factoren (2)

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

1. \(-50b^{9}-80b^{6}-32b^{3}\)
2. \(49p^{15}+14p^{10}x+p^{5}x^2\)
3. \(-75q^{6}+12q^{2}\)
4. \(32x^{15}+80x^{10}+50x^{5}\)
5. \(294b^{4}-252b^{3}+54b^{2}\)
6. \(-6s^{4}+150s^{2}\)
7. \(245s^{4}+70s^{3}+5s^{2}\)
8. \(-6b^{7}-36b^{6}-54b^{5}\)
9. \(3b^{7}+12b^{6}+12b^{5}\)
10. \(5x^{4}+90x^{3}+405x^{2}\)
11. \(-8y^{8}+2y^{4}\)
12. \(-12b^{12}-12b^{8}q-3b^{4}q^2\)

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

Verbetersleutel

1. \(-50b^{9}-80b^{6}-32b^{3}=-2b^{3}(25b^{6}+40b^3+16)=-2b^{3}(5b^3+4)^2\)
2. \(49p^{15}+14p^{10}x+p^{5}x^2=p^{5}(49p^{10}+14p^5x+x^2)=p^{5}(7p^5+x)^2\)
3. \(-75q^{6}+12q^{2}=-3q^{2}(25q^{4}-4)=-3q^{2}(5q^2+2)(5q^2-2)\)
4. \(32x^{15}+80x^{10}+50x^{5}=2x^{5}(16x^{10}+40x^5+25)=2x^{5}(4x^5+5)^2\)
5. \(294b^{4}-252b^{3}+54b^{2}=6b^{2}(49b^{2}-42b+9)=6b^{2}(7b-3)^2\)
6. \(-6s^{4}+150s^{2}=-6s^{2}(s^2-25)=-6s^{2}(s+5)(s-5)\)
7. \(245s^{4}+70s^{3}+5s^{2}=5s^{2}(49s^{2}+14s+1)=5s^{2}(7s+1)^2\)
8. \(-6b^{7}-36b^{6}-54b^{5}=-6b^{5}(b^2+6b+9)=-6b^{5}(b+3)^2\)
9. \(3b^{7}+12b^{6}+12b^{5}=3b^{5}(b^2+4b+4)=3b^{5}(b+2)^2\)
10. \(5x^{4}+90x^{3}+405x^{2}=5x^{2}(x^2+18x+81)=5x^{2}(x+9)^2\)
11. \(-8y^{8}+2y^{4}=-2y^{4}(4y^{4}-1)=-2y^{4}(2y^2+1)(2y^2-1)\)
12. \(-12b^{12}-12b^{8}q-3b^{4}q^2=-3b^{4}(4b^{8}+4b^4q+q^2)=-3b^{4}(2b^4+q)^2\)