Ontbinden in factoren (2)

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

1. \(-3s^{4}+147s^{2}\)
2. \(6p^{5}+24p^{4}+24p^{3}\)
3. \(12q^{17}-147q^{3}\)
4. \(125y^{11}-5y^{5}\)
5. \(a^{4}-36a^{2}\)
6. \(108q^{6}+36q^{4}s+3q^{2}s^2\)
7. \(25q^{7}-9q^{5}\)
8. \(8a^{17}-98a^{5}\)
9. \(49x^{11}+28x^{7}y+4x^{3}y^2\)
10. \(-108p^{9}-36p^{6}-3p^{3}\)
11. \(54s^{14}-180s^{9}x+150s^{4}x^2\)
12. \(24s^{4}+24s^{3}+6s^{2}\)

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

Verbetersleutel

1. \(-3s^{4}+147s^{2}=-3s^{2}(s^2-49)=-3s^{2}(s+7)(s-7)\)
2. \(6p^{5}+24p^{4}+24p^{3}=6p^{3}(p^2+4p+4)=6p^{3}(p+2)^2\)
3. \(12q^{17}-147q^{3}=3q^{3}(4q^{14}-49)=3q^{3}(2q^7+7)(2q^7-7)\)
4. \(125y^{11}-5y^{5}=5y^{5}(25y^{6}-1)=5y^{5}(5y^3+1)(5y^3-1)\)
5. \(a^{4}-36a^{2}=a^{2}(a^2-36)=a^{2}(a-6)(a+6)\)
6. \(108q^{6}+36q^{4}s+3q^{2}s^2=3q^{2}(36q^{4}+12q^2s+s^2)=3q^{2}(6q^2+s)^2\)
7. \(25q^{7}-9q^{5}=q^{5}(25q^{2}-9)=q^{5}(5q+3)(5q-3)\)
8. \(8a^{17}-98a^{5}=2a^{5}(4a^{12}-49)=2a^{5}(2a^6+7)(2a^6-7)\)
9. \(49x^{11}+28x^{7}y+4x^{3}y^2=x^{3}(49x^{8}+28x^4y+4y^2)=x^{3}(7x^4+2y)^2\)
10. \(-108p^{9}-36p^{6}-3p^{3}=-3p^{3}(36p^{6}+12p^3+1)=-3p^{3}(6p^3+1)^2\)
11. \(54s^{14}-180s^{9}x+150s^{4}x^2=6s^{4}(9s^{10}-30s^5x+25x^2)=6s^{4}(3s^5-5x)^2\)
12. \(24s^{4}+24s^{3}+6s^{2}=6s^{2}(4s^{2}+4s+1)=6s^{2}(2s+1)^2\)