Ontbinden in factoren (2)

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

1. \(-108y^{7}-36y^{5}-3y^{3}\)
2. \(x^{6}-4x^{5}+4x^{4}\)
3. \(-2x^{6}+8x^{4}\)
4. \(-27x^{5}+144x^{4}-192x^{3}\)
5. \(48q^{4}-168q^{3}+147q^{2}\)
6. \(245a^{13}-140a^{9}+20a^{5}\)
7. \(36s^{14}+60s^{9}+25s^{4}\)
8. \(-20q^{15}-20q^{10}y-5q^{5}y^2\)
9. \(8q^{10}+24q^{7}+18q^{4}\)
10. \(-48b^{4}+27b^{2}\)
11. \(-64y^{11}-16y^{8}-y^{5}\)
12. \(-294x^{13}+252x^{9}y-54x^{5}y^2\)

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

Verbetersleutel

1. \(-108y^{7}-36y^{5}-3y^{3}=-3y^{3}(36y^{4}+12y^2+1)=-3y^{3}(6y^2+1)^2\)
2. \(x^{6}-4x^{5}+4x^{4}=x^{4}(x^2-4x+4)=x^{4}(x-2)^2\)
3. \(-2x^{6}+8x^{4}=-2x^{4}(x^2-4)=-2x^{4}(x+2)(x-2)\)
4. \(-27x^{5}+144x^{4}-192x^{3}=-3x^{3}(9x^{2}-48x+64)=-3x^{3}(3x-8)^2\)
5. \(48q^{4}-168q^{3}+147q^{2}=3q^{2}(16q^{2}-56q+49)=3q^{2}(4q-7)^2\)
6. \(245a^{13}-140a^{9}+20a^{5}=5a^{5}(49a^{8}-28a^4+4)=5a^{5}(7a^4-2)^2\)
7. \(36s^{14}+60s^{9}+25s^{4}=s^{4}(36s^{10}+60s^5+25)=s^{4}(6s^5+5)^2\)
8. \(-20q^{15}-20q^{10}y-5q^{5}y^2=-5q^{5}(4q^{10}+4q^5y+y^2)=-5q^{5}(2q^5+y)^2\)
9. \(8q^{10}+24q^{7}+18q^{4}=2q^{4}(4q^{6}+12q^3+9)=2q^{4}(2q^3+3)^2\)
10. \(-48b^{4}+27b^{2}=-3b^{2}(16b^{2}-9)=-3b^{2}(4b+3)(4b-3)\)
11. \(-64y^{11}-16y^{8}-y^{5}=-y^{5}(64y^{6}+16y^3+1)=-y^{5}(8y^3+1)^2\)
12. \(-294x^{13}+252x^{9}y-54x^{5}y^2=-6x^{5}(49x^{8}-42x^4y+9y^2)=-6x^{5}(7x^4-3y)^2\)