Ontbinden in factoren (2)

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

1. \(-24y^{4}+150y^{2}\)
2. \(-96p^{9}+150p^{3}\)
3. \(216p^{9}+72p^{7}y+6p^{5}y^2\)
4. \(-49s^{5}-84s^{4}-36s^{3}\)
5. \(-2a^{5}+36a^{4}-162a^{3}\)
6. \(150b^{20}-6b^{4}\)
7. \(-125b^{15}-50b^{10}x-5b^{5}x^2\)
8. \(3p^{5}+30p^{4}+75p^{3}\)
9. \(-24s^{5}-24s^{4}-6s^{3}\)
10. \(6x^{5}-6x^{3}\)
11. \(-6b^{6}-12b^{5}-6b^{4}\)
12. \(-6s^{4}+84s^{3}-294s^{2}\)

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

Verbetersleutel

1. \(-24y^{4}+150y^{2}=-6y^{2}(4y^{2}-25)=-6y^{2}(2y+5)(2y-5)\)
2. \(-96p^{9}+150p^{3}=-6p^{3}(16p^{6}-25)=-6p^{3}(4p^3+5)(4p^3-5)\)
3. \(216p^{9}+72p^{7}y+6p^{5}y^2=6p^{5}(36p^{4}+12p^2y+y^2)=6p^{5}(6p^2+y)^2\)
4. \(-49s^{5}-84s^{4}-36s^{3}=-s^{3}(49s^{2}+84s+36)=-s^{3}(7s+6)^2\)
5. \(-2a^{5}+36a^{4}-162a^{3}=-2a^{3}(a^2-18a+81)=-2a^{3}(a-9)^2\)
6. \(150b^{20}-6b^{4}=6b^{4}(25b^{16}-1)=6b^{4}(5b^8+1)(5b^8-1)\)
7. \(-125b^{15}-50b^{10}x-5b^{5}x^2=-5b^{5}(25b^{10}+10b^5x+x^2)=-5b^{5}(5b^5+x)^2\)
8. \(3p^{5}+30p^{4}+75p^{3}=3p^{3}(p^2+10p+25)=3p^{3}(p+5)^2\)
9. \(-24s^{5}-24s^{4}-6s^{3}=-6s^{3}(4s^{2}+4s+1)=-6s^{3}(2s+1)^2\)
10. \(6x^{5}-6x^{3}=6x^{3}(x^2-1)=6x^{3}(x-1)(x+1)\)
11. \(-6b^{6}-12b^{5}-6b^{4}=-6b^{4}(b^2+2b+1)=-6b^{4}(b+1)^2\)
12. \(-6s^{4}+84s^{3}-294s^{2}=-6s^{2}(s^2-14s+49)=-6s^{2}(s-7)^2\)