Ontbinden in factoren (2)

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

1. \(-2x^{7}+72x^{5}\)
2. \(-32s^{7}-112s^{6}-98s^{5}\)
3. \(-96x^{14}+54x^{4}\)
4. \(3x^{6}-75x^{4}\)
5. \(-64b^{10}-16b^{7}y-b^{4}y^2\)
6. \(12y^{11}+12y^{8}+3y^{5}\)
7. \(5p^{5}-125p^{3}\)
8. \(24s^{19}-6s^{5}\)
9. \(5q^{5}-60q^{4}+180q^{3}\)
10. \(-12y^{9}-12y^{7}-3y^{5}\)
11. \(25b^{8}+30b^{5}s+9b^{2}s^2\)
12. \(-5y^{6}+125y^{4}\)

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

Verbetersleutel

1. \(-2x^{7}+72x^{5}=-2x^{5}(x^2-36)=-2x^{5}(x-6)(x+6)\)
2. \(-32s^{7}-112s^{6}-98s^{5}=-2s^{5}(16s^{2}+56s+49)=-2s^{5}(4s+7)^2\)
3. \(-96x^{14}+54x^{4}=-6x^{4}(16x^{10}-9)=-6x^{4}(4x^5+3)(4x^5-3)\)
4. \(3x^{6}-75x^{4}=3x^{4}(x^2-25)=3x^{4}(x-5)(x+5)\)
5. \(-64b^{10}-16b^{7}y-b^{4}y^2=-b^{4}(64b^{6}+16b^3y+y^2)=-b^{4}(8b^3+y)^2\)
6. \(12y^{11}+12y^{8}+3y^{5}=3y^{5}(4y^{6}+4y^3+1)=3y^{5}(2y^3+1)^2\)
7. \(5p^{5}-125p^{3}=5p^{3}(p^2-25)=5p^{3}(p+5)(p-5)\)
8. \(24s^{19}-6s^{5}=6s^{5}(4s^{14}-1)=6s^{5}(2s^7+1)(2s^7-1)\)
9. \(5q^{5}-60q^{4}+180q^{3}=5q^{3}(q^2-12q+36)=5q^{3}(q-6)^2\)
10. \(-12y^{9}-12y^{7}-3y^{5}=-3y^{5}(4y^{4}+4y^2+1)=-3y^{5}(2y^2+1)^2\)
11. \(25b^{8}+30b^{5}s+9b^{2}s^2=b^{2}(25b^{6}+30b^3s+9s^2)=b^{2}(5b^3+3s)^2\)
12. \(-5y^{6}+125y^{4}=-5y^{4}(y^2-25)=-5y^{4}(y+5)(y-5)\)