Ontbinden in factoren (2)

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

1. \(-80x^{10}+245x^{4}\)
2. \(192b^{9}+144b^{7}x+27b^{5}x^2\)
3. \(a^{4}-25a^{2}\)
4. \(25b^{7}-20b^{6}+4b^{5}\)
5. \(-5x^{6}+320x^{4}\)
6. \(147q^{7}+210q^{6}+75q^{5}\)
7. \(2q^{7}+8q^{6}+8q^{5}\)
8. \(-2y^{7}+32y^{6}-128y^{5}\)
9. \(a^{5}-8a^{4}+16a^{3}\)
10. \(245p^{5}+210p^{4}+45p^{3}\)
11. \(24x^{8}-54x^{2}\)
12. \(125b^{4}-245b^{2}\)

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

Verbetersleutel

1. \(-80x^{10}+245x^{4}=-5x^{4}(16x^{6}-49)=-5x^{4}(4x^3+7)(4x^3-7)\)
2. \(192b^{9}+144b^{7}x+27b^{5}x^2=3b^{5}(64b^{4}+48b^2x+9x^2)=3b^{5}(8b^2+3x)^2\)
3. \(a^{4}-25a^{2}=a^{2}(a^2-25)=a^{2}(a-5)(a+5)\)
4. \(25b^{7}-20b^{6}+4b^{5}=b^{5}(25b^{2}-20b+4)=b^{5}(5b-2)^2\)
5. \(-5x^{6}+320x^{4}=-5x^{4}(x^2-64)=-5x^{4}(x+8)(x-8)\)
6. \(147q^{7}+210q^{6}+75q^{5}=3q^{5}(49q^{2}+70q+25)=3q^{5}(7q+5)^2\)
7. \(2q^{7}+8q^{6}+8q^{5}=2q^{5}(q^2+4q+4)=2q^{5}(q+2)^2\)
8. \(-2y^{7}+32y^{6}-128y^{5}=-2y^{5}(y^2-16y+64)=-2y^{5}(y-8)^2\)
9. \(a^{5}-8a^{4}+16a^{3}=a^{3}(a^2-8a+16)=a^{3}(a-4)^2\)
10. \(245p^{5}+210p^{4}+45p^{3}=5p^{3}(49p^{2}+42p+9)=5p^{3}(7p+3)^2\)
11. \(24x^{8}-54x^{2}=6x^{2}(4x^{6}-9)=6x^{2}(2x^3+3)(2x^3-3)\)
12. \(125b^{4}-245b^{2}=5b^{2}(25b^{2}-49)=5b^{2}(5b+7)(5b-7)\)