Ontbinden in factoren (2)

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

1. \(-2b^{7}+32b^{6}-128b^{5}\)
2. \(80q^{10}-245q^{2}\)
3. \(-25s^{4}+s^{2}\)
4. \(-y^{5}-4y^{4}-4y^{3}\)
5. \(2x^{7}-72x^{5}\)
6. \(192q^{11}+48q^{7}s+3q^{3}s^2\)
7. \(-45p^{15}+5p^{5}\)
8. \(-x^{5}+16x^{4}-64x^{3}\)
9. \(-y^{5}+y^{3}\)
10. \(6p^{5}-36p^{4}+54p^{3}\)
11. \(-108s^{7}+147s^{5}\)
12. \(245b^{6}+70b^{5}+5b^{4}\)

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

Verbetersleutel

1. \(-2b^{7}+32b^{6}-128b^{5}=-2b^{5}(b^2-16b+64)=-2b^{5}(b-8)^2\)
2. \(80q^{10}-245q^{2}=5q^{2}(16q^{8}-49)=5q^{2}(4q^4+7)(4q^4-7)\)
3. \(-25s^{4}+s^{2}=-s^{2}(25s^{2}-1)=-s^{2}(5s+1)(5s-1)\)
4. \(-y^{5}-4y^{4}-4y^{3}=-y^{3}(y^2+4y+4)=-y^{3}(y+2)^2\)
5. \(2x^{7}-72x^{5}=2x^{5}(x^2-36)=2x^{5}(x+6)(x-6)\)
6. \(192q^{11}+48q^{7}s+3q^{3}s^2=3q^{3}(64q^{8}+16q^4s+s^2)=3q^{3}(8q^4+s)^2\)
7. \(-45p^{15}+5p^{5}=-5p^{5}(9p^{10}-1)=-5p^{5}(3p^5+1)(3p^5-1)\)
8. \(-x^{5}+16x^{4}-64x^{3}=-x^{3}(x^2-16x+64)=-x^{3}(x-8)^2\)
9. \(-y^{5}+y^{3}=-y^{3}(y^2-1)=-y^{3}(y-1)(y+1)\)
10. \(6p^{5}-36p^{4}+54p^{3}=6p^{3}(p^2-6p+9)=6p^{3}(p-3)^2\)
11. \(-108s^{7}+147s^{5}=-3s^{5}(36s^{2}-49)=-3s^{5}(6s+7)(6s-7)\)
12. \(245b^{6}+70b^{5}+5b^{4}=5b^{4}(49b^{2}+14b+1)=5b^{4}(7b+1)^2\)