Ontbinden in factoren (2)

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

1. \(54q^{7}-180q^{5}x+150q^{3}x^2\)
2. \(-6x^{4}-84x^{3}-294x^{2}\)
3. \(5y^{4}+30y^{3}+45y^{2}\)
4. \(-6s^{6}+216s^{4}\)
5. \(54b^{6}-6b^{4}\)
6. \(27b^{9}+90b^{7}p+75b^{5}p^2\)
7. \(48p^{7}-168p^{6}+147p^{5}\)
8. \(-24x^{7}+294x^{3}\)
9. \(9b^{8}+30b^{5}+25b^{2}\)
10. \(24a^{6}-6a^{4}\)
11. \(-50q^{8}-20q^{5}-2q^{2}\)
12. \(-6a^{5}-48a^{4}-96a^{3}\)

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

Verbetersleutel

1. \(54q^{7}-180q^{5}x+150q^{3}x^2=6q^{3}(9q^{4}-30q^2x+25x^2)=6q^{3}(3q^2-5x)^2\)
2. \(-6x^{4}-84x^{3}-294x^{2}=-6x^{2}(x^2+14x+49)=-6x^{2}(x+7)^2\)
3. \(5y^{4}+30y^{3}+45y^{2}=5y^{2}(y^2+6y+9)=5y^{2}(y+3)^2\)
4. \(-6s^{6}+216s^{4}=-6s^{4}(s^2-36)=-6s^{4}(s+6)(s-6)\)
5. \(54b^{6}-6b^{4}=6b^{4}(9b^{2}-1)=6b^{4}(3b+1)(3b-1)\)
6. \(27b^{9}+90b^{7}p+75b^{5}p^2=3b^{5}(9b^{4}+30b^2p+25p^2)=3b^{5}(3b^2+5p)^2\)
7. \(48p^{7}-168p^{6}+147p^{5}=3p^{5}(16p^{2}-56p+49)=3p^{5}(4p-7)^2\)
8. \(-24x^{7}+294x^{3}=-6x^{3}(4x^{4}-49)=-6x^{3}(2x^2+7)(2x^2-7)\)
9. \(9b^{8}+30b^{5}+25b^{2}=b^{2}(9b^{6}+30b^3+25)=b^{2}(3b^3+5)^2\)
10. \(24a^{6}-6a^{4}=6a^{4}(4a^{2}-1)=6a^{4}(2a+1)(2a-1)\)
11. \(-50q^{8}-20q^{5}-2q^{2}=-2q^{2}(25q^{6}+10q^3+1)=-2q^{2}(5q^3+1)^2\)
12. \(-6a^{5}-48a^{4}-96a^{3}=-6a^{3}(a^2+8a+16)=-6a^{3}(a+4)^2\)