Ontbinden in factoren (2)

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

1. \(-6x^{4}-108x^{3}-486x^{2}\)
2. \(32s^{16}-50s^{4}\)
3. \(16p^{10}+40p^{6}x+25p^{2}x^2\)
4. \(-6p^{6}+48p^{5}-96p^{4}\)
5. \(-192q^{7}-48q^{5}-3q^{3}\)
6. \(-5x^{7}+320x^{5}\)
7. \(9b^{11}-12b^{7}y+4b^{3}y^2\)
8. \(3b^{5}-12b^{3}\)
9. \(-25b^{9}+40b^{6}x-16b^{3}x^2\)
10. \(50y^{8}-72y^{2}\)
11. \(294y^{5}-252y^{4}+54y^{3}\)
12. \(-3q^{5}+108q^{3}\)

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

Verbetersleutel

1. \(-6x^{4}-108x^{3}-486x^{2}=-6x^{2}(x^2+18x+81)=-6x^{2}(x+9)^2\)
2. \(32s^{16}-50s^{4}=2s^{4}(16s^{12}-25)=2s^{4}(4s^6+5)(4s^6-5)\)
3. \(16p^{10}+40p^{6}x+25p^{2}x^2=p^{2}(16p^{8}+40p^4x+25x^2)=p^{2}(4p^4+5x)^2\)
4. \(-6p^{6}+48p^{5}-96p^{4}=-6p^{4}(p^2-8p+16)=-6p^{4}(p-4)^2\)
5. \(-192q^{7}-48q^{5}-3q^{3}=-3q^{3}(64q^{4}+16q^2+1)=-3q^{3}(8q^2+1)^2\)
6. \(-5x^{7}+320x^{5}=-5x^{5}(x^2-64)=-5x^{5}(x-8)(x+8)\)
7. \(9b^{11}-12b^{7}y+4b^{3}y^2=b^{3}(9b^{8}-12b^4y+4y^2)=b^{3}(3b^4-2y)^2\)
8. \(3b^{5}-12b^{3}=3b^{3}(b^2-4)=3b^{3}(b+2)(b-2)\)
9. \(-25b^{9}+40b^{6}x-16b^{3}x^2=-b^{3}(25b^{6}-40b^3x+16x^2)=-b^{3}(5b^3-4x)^2\)
10. \(50y^{8}-72y^{2}=2y^{2}(25y^{6}-36)=2y^{2}(5y^3+6)(5y^3-6)\)
11. \(294y^{5}-252y^{4}+54y^{3}=6y^{3}(49y^{2}-42y+9)=6y^{3}(7y-3)^2\)
12. \(-3q^{5}+108q^{3}=-3q^{3}(q^2-36)=-3q^{3}(q-6)(q+6)\)