Ontbinden in factoren (2)

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

1. \(-64x^{5}+112x^{4}-49x^{3}\)
2. \(5q^{5}-20q^{3}\)
3. \(-9s^{5}+s^{3}\)
4. \(-50s^{11}-120s^{8}y-72s^{5}y^2\)
5. \(-3x^{4}+30x^{3}-75x^{2}\)
6. \(192s^{7}-336s^{5}+147s^{3}\)
7. \(-50q^{9}+140q^{7}y-98q^{5}y^2\)
8. \(-98p^{9}+168p^{7}q-72p^{5}q^2\)
9. \(4b^{16}-b^{2}\)
10. \(25b^{14}-49b^{2}\)
11. \(-45y^{8}+150y^{5}-125y^{2}\)
12. \(-3q^{7}+48q^{5}\)

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

Verbetersleutel

1. \(-64x^{5}+112x^{4}-49x^{3}=-x^{3}(64x^{2}-112x+49)=-x^{3}(8x-7)^2\)
2. \(5q^{5}-20q^{3}=5q^{3}(q^2-4)=5q^{3}(q-2)(q+2)\)
3. \(-9s^{5}+s^{3}=-s^{3}(9s^{2}-1)=-s^{3}(3s+1)(3s-1)\)
4. \(-50s^{11}-120s^{8}y-72s^{5}y^2=-2s^{5}(25s^{6}+60s^3y+36y^2)=-2s^{5}(5s^3+6y)^2\)
5. \(-3x^{4}+30x^{3}-75x^{2}=-3x^{2}(x^2-10x+25)=-3x^{2}(x-5)^2\)
6. \(192s^{7}-336s^{5}+147s^{3}=3s^{3}(64s^{4}-112s^2+49)=3s^{3}(8s^2-7)^2\)
7. \(-50q^{9}+140q^{7}y-98q^{5}y^2=-2q^{5}(25q^{4}-70q^2y+49y^2)=-2q^{5}(5q^2-7y)^2\)
8. \(-98p^{9}+168p^{7}q-72p^{5}q^2=-2p^{5}(49p^{4}-84p^2q+36q^2)=-2p^{5}(7p^2-6q)^2\)
9. \(4b^{16}-b^{2}=b^{2}(4b^{14}-1)=b^{2}(2b^7+1)(2b^7-1)\)
10. \(25b^{14}-49b^{2}=b^{2}(25b^{12}-49)=b^{2}(5b^6+7)(5b^6-7)\)
11. \(-45y^{8}+150y^{5}-125y^{2}=-5y^{2}(9y^{6}-30y^3+25)=-5y^{2}(3y^3-5)^2\)
12. \(-3q^{7}+48q^{5}=-3q^{5}(q^2-16)=-3q^{5}(q-4)(q+4)\)