Ontbinden in factoren (2)

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

1. \(5y^{4}-70y^{3}+245y^{2}\)
2. \(-p^{5}-6p^{4}-9p^{3}\)
3. \(320a^{11}-560a^{8}y+245a^{5}y^2\)
4. \(-3b^{7}+108b^{5}\)
5. \(-192p^{14}+336p^{9}x-147p^{4}x^2\)
6. \(45p^{7}-5p^{3}\)
7. \(-48a^{5}-120a^{4}-75a^{3}\)
8. \(5p^{4}-5p^{2}\)
9. \(6q^{4}-24q^{2}\)
10. \(-54y^{14}-36y^{9}-6y^{4}\)
11. \(-5q^{4}+20q^{2}\)
12. \(-27s^{6}-36s^{5}-12s^{4}\)

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

Verbetersleutel

1. \(5y^{4}-70y^{3}+245y^{2}=5y^{2}(y^2-14y+49)=5y^{2}(y-7)^2\)
2. \(-p^{5}-6p^{4}-9p^{3}=-p^{3}(p^2+6p+9)=-p^{3}(p+3)^2\)
3. \(320a^{11}-560a^{8}y+245a^{5}y^2=5a^{5}(64a^{6}-112a^3y+49y^2)=5a^{5}(8a^3-7y)^2\)
4. \(-3b^{7}+108b^{5}=-3b^{5}(b^2-36)=-3b^{5}(b-6)(b+6)\)
5. \(-192p^{14}+336p^{9}x-147p^{4}x^2=-3p^{4}(64p^{10}-112p^5x+49x^2)=-3p^{4}(8p^5-7x)^2\)
6. \(45p^{7}-5p^{3}=5p^{3}(9p^{4}-1)=5p^{3}(3p^2+1)(3p^2-1)\)
7. \(-48a^{5}-120a^{4}-75a^{3}=-3a^{3}(16a^{2}+40a+25)=-3a^{3}(4a+5)^2\)
8. \(5p^{4}-5p^{2}=5p^{2}(p^2-1)=5p^{2}(p-1)(p+1)\)
9. \(6q^{4}-24q^{2}=6q^{2}(q^2-4)=6q^{2}(q-2)(q+2)\)
10. \(-54y^{14}-36y^{9}-6y^{4}=-6y^{4}(9y^{10}+6y^5+1)=-6y^{4}(3y^5+1)^2\)
11. \(-5q^{4}+20q^{2}=-5q^{2}(q^2-4)=-5q^{2}(q+2)(q-2)\)
12. \(-27s^{6}-36s^{5}-12s^{4}=-3s^{4}(9s^{2}+12s+4)=-3s^{4}(3s+2)^2\)