Ontbinden in factoren (2)

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

1. \(-5x^{4}+70x^{3}-245x^{2}\)
2. \(-4s^{10}-4s^{6}-s^{2}\)
3. \(75q^{4}-270q^{3}+243q^{2}\)
4. \(b^{5}-10b^{4}+25b^{3}\)
5. \(-16a^{7}-40a^{5}x-25a^{3}x^2\)
6. \(72b^{6}+24b^{4}+2b^{2}\)
7. \(96a^{11}+240a^{8}b+150a^{5}b^2\)
8. \(3b^{6}-54b^{5}+243b^{4}\)
9. \(-27y^{14}+90y^{9}-75y^{4}\)
10. \(-64x^{4}-16x^{3}-x^{2}\)
11. \(125b^{6}+150b^{5}+45b^{4}\)
12. \(320x^{10}+240x^{7}+45x^{4}\)

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

Verbetersleutel

1. \(-5x^{4}+70x^{3}-245x^{2}=-5x^{2}(x^2-14x+49)=-5x^{2}(x-7)^2\)
2. \(-4s^{10}-4s^{6}-s^{2}=-s^{2}(4s^{8}+4s^4+1)=-s^{2}(2s^4+1)^2\)
3. \(75q^{4}-270q^{3}+243q^{2}=3q^{2}(25q^{2}-90q+81)=3q^{2}(5q-9)^2\)
4. \(b^{5}-10b^{4}+25b^{3}=b^{3}(b^2-10b+25)=b^{3}(b-5)^2\)
5. \(-16a^{7}-40a^{5}x-25a^{3}x^2=-a^{3}(16a^{4}+40a^2x+25x^2)=-a^{3}(4a^2+5x)^2\)
6. \(72b^{6}+24b^{4}+2b^{2}=2b^{2}(36b^{4}+12b^2+1)=2b^{2}(6b^2+1)^2\)
7. \(96a^{11}+240a^{8}b+150a^{5}b^2=6a^{5}(16a^{6}+40a^3b+25b^2)=6a^{5}(4a^3+5b)^2\)
8. \(3b^{6}-54b^{5}+243b^{4}=3b^{4}(b^2-18b+81)=3b^{4}(b-9)^2\)
9. \(-27y^{14}+90y^{9}-75y^{4}=-3y^{4}(9y^{10}-30y^5+25)=-3y^{4}(3y^5-5)^2\)
10. \(-64x^{4}-16x^{3}-x^{2}=-x^{2}(64x^{2}+16x+1)=-x^{2}(8x+1)^2\)
11. \(125b^{6}+150b^{5}+45b^{4}=5b^{4}(25b^{2}+30b+9)=5b^{4}(5b+3)^2\)
12. \(320x^{10}+240x^{7}+45x^{4}=5x^{4}(64x^{6}+48x^3+9)=5x^{4}(8x^3+3)^2\)