Ontbinden in factoren (2)

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

1. \(6p^{7}-36p^{6}+54p^{5}\)
2. \(-36s^{5}+s^{3}\)
3. \(108p^{7}+180p^{6}+75p^{5}\)
4. \(294b^{6}-252b^{4}y+54b^{2}y^2\)
5. \(-5a^{7}+5a^{5}\)
6. \(-5a^{5}-40a^{4}-80a^{3}\)
7. \(8y^{4}+56y^{3}+98y^{2}\)
8. \(-2a^{7}+2a^{5}\)
9. \(54q^{8}+36q^{6}+6q^{4}\)
10. \(x^{5}-8x^{4}+16x^{3}\)
11. \(-2s^{5}+8s^{3}\)
12. \(-36s^{9}+60s^{7}y-25s^{5}y^2\)

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

Verbetersleutel

1. \(6p^{7}-36p^{6}+54p^{5}=6p^{5}(p^2-6p+9)=6p^{5}(p-3)^2\)
2. \(-36s^{5}+s^{3}=-s^{3}(36s^{2}-1)=-s^{3}(6s+1)(6s-1)\)
3. \(108p^{7}+180p^{6}+75p^{5}=3p^{5}(36p^{2}+60p+25)=3p^{5}(6p+5)^2\)
4. \(294b^{6}-252b^{4}y+54b^{2}y^2=6b^{2}(49b^{4}-42b^2y+9y^2)=6b^{2}(7b^2-3y)^2\)
5. \(-5a^{7}+5a^{5}=-5a^{5}(a^2-1)=-5a^{5}(a+1)(a-1)\)
6. \(-5a^{5}-40a^{4}-80a^{3}=-5a^{3}(a^2+8a+16)=-5a^{3}(a+4)^2\)
7. \(8y^{4}+56y^{3}+98y^{2}=2y^{2}(4y^{2}+28y+49)=2y^{2}(2y+7)^2\)
8. \(-2a^{7}+2a^{5}=-2a^{5}(a^2-1)=-2a^{5}(a-1)(a+1)\)
9. \(54q^{8}+36q^{6}+6q^{4}=6q^{4}(9q^{4}+6q^2+1)=6q^{4}(3q^2+1)^2\)
10. \(x^{5}-8x^{4}+16x^{3}=x^{3}(x^2-8x+16)=x^{3}(x-4)^2\)
11. \(-2s^{5}+8s^{3}=-2s^{3}(s^2-4)=-2s^{3}(s-2)(s+2)\)
12. \(-36s^{9}+60s^{7}y-25s^{5}y^2=-s^{5}(36s^{4}-60s^2y+25y^2)=-s^{5}(6s^2-5y)^2\)