Ontbinden in factoren (2)

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

1. \(98s^{7}-168s^{6}+72s^{5}\)
2. \(9q^{6}-30q^{4}+25q^{2}\)
3. \(-96p^{5}+294p^{3}\)
4. \(-3s^{6}+192s^{4}\)
5. \(25a^{5}-40a^{4}+16a^{3}\)
6. \(-6b^{5}+12b^{4}-6b^{3}\)
7. \(-6x^{4}+36x^{3}-54x^{2}\)
8. \(5b^{4}+30b^{3}+45b^{2}\)
9. \(3x^{4}-18x^{3}+27x^{2}\)
10. \(24x^{4}+72x^{3}+54x^{2}\)
11. \(54q^{11}+144q^{8}x+96q^{5}x^2\)
12. \(-20q^{6}+245q^{4}\)

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

Verbetersleutel

1. \(98s^{7}-168s^{6}+72s^{5}=2s^{5}(49s^{2}-84s+36)=2s^{5}(7s-6)^2\)
2. \(9q^{6}-30q^{4}+25q^{2}=q^{2}(9q^{4}-30q^2+25)=q^{2}(3q^2-5)^2\)
3. \(-96p^{5}+294p^{3}=-6p^{3}(16p^{2}-49)=-6p^{3}(4p+7)(4p-7)\)
4. \(-3s^{6}+192s^{4}=-3s^{4}(s^2-64)=-3s^{4}(s+8)(s-8)\)
5. \(25a^{5}-40a^{4}+16a^{3}=a^{3}(25a^{2}-40a+16)=a^{3}(5a-4)^2\)
6. \(-6b^{5}+12b^{4}-6b^{3}=-6b^{3}(b^2-2b+1)=-6b^{3}(b-1)^2\)
7. \(-6x^{4}+36x^{3}-54x^{2}=-6x^{2}(x^2-6x+9)=-6x^{2}(x-3)^2\)
8. \(5b^{4}+30b^{3}+45b^{2}=5b^{2}(b^2+6b+9)=5b^{2}(b+3)^2\)
9. \(3x^{4}-18x^{3}+27x^{2}=3x^{2}(x^2-6x+9)=3x^{2}(x-3)^2\)
10. \(24x^{4}+72x^{3}+54x^{2}=6x^{2}(4x^{2}+12x+9)=6x^{2}(2x+3)^2\)
11. \(54q^{11}+144q^{8}x+96q^{5}x^2=6q^{5}(9q^{6}+24q^3x+16x^2)=6q^{5}(3q^3+4x)^2\)
12. \(-20q^{6}+245q^{4}=-5q^{4}(4q^{2}-49)=-5q^{4}(2q+7)(2q-7)\)