Ontbinden in factoren (2)

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

1. \(-5p^{6}+20p^{5}-20p^{4}\)
2. \(-216q^{12}+294q^{4}\)
3. \(-9a^{15}-12a^{10}b-4a^{5}b^2\)
4. \(-98q^{11}-112q^{8}-32q^{5}\)
5. \(-72b^{10}+98b^{4}\)
6. \(x^{7}+12x^{6}+36x^{5}\)
7. \(32p^{12}+48p^{7}x+18p^{2}x^2\)
8. \(72y^{8}-120y^{5}+50y^{2}\)
9. \(45b^{13}+120b^{8}y+80b^{3}y^2\)
10. \(48q^{5}+24q^{4}+3q^{3}\)
11. \(-p^{6}-10p^{5}-25p^{4}\)
12. \(-4a^{12}-4a^{7}q-a^{2}q^2\)

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

Verbetersleutel

1. \(-5p^{6}+20p^{5}-20p^{4}=-5p^{4}(p^2-4p+4)=-5p^{4}(p-2)^2\)
2. \(-216q^{12}+294q^{4}=-6q^{4}(36q^{8}-49)=-6q^{4}(6q^4+7)(6q^4-7)\)
3. \(-9a^{15}-12a^{10}b-4a^{5}b^2=-a^{5}(9a^{10}+12a^5b+4b^2)=-a^{5}(3a^5+2b)^2\)
4. \(-98q^{11}-112q^{8}-32q^{5}=-2q^{5}(49q^{6}+56q^3+16)=-2q^{5}(7q^3+4)^2\)
5. \(-72b^{10}+98b^{4}=-2b^{4}(36b^{6}-49)=-2b^{4}(6b^3+7)(6b^3-7)\)
6. \(x^{7}+12x^{6}+36x^{5}=x^{5}(x^2+12x+36)=x^{5}(x+6)^2\)
7. \(32p^{12}+48p^{7}x+18p^{2}x^2=2p^{2}(16p^{10}+24p^5x+9x^2)=2p^{2}(4p^5+3x)^2\)
8. \(72y^{8}-120y^{5}+50y^{2}=2y^{2}(36y^{6}-60y^3+25)=2y^{2}(6y^3-5)^2\)
9. \(45b^{13}+120b^{8}y+80b^{3}y^2=5b^{3}(9b^{10}+24b^5y+16y^2)=5b^{3}(3b^5+4y)^2\)
10. \(48q^{5}+24q^{4}+3q^{3}=3q^{3}(16q^{2}+8q+1)=3q^{3}(4q+1)^2\)
11. \(-p^{6}-10p^{5}-25p^{4}=-p^{4}(p^2+10p+25)=-p^{4}(p+5)^2\)
12. \(-4a^{12}-4a^{7}q-a^{2}q^2=-a^{2}(4a^{10}+4a^5q+q^2)=-a^{2}(2a^5+q)^2\)