Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(24y^{18}-294y^{4}\)
2. \(125s^{12}-20s^{2}\)
3. \(-320p^{7}+560p^{6}-245p^{5}\)
4. \(-p^{7}+6p^{6}-9p^{5}\)
5. \(5p^{4}-180p^{2}\)
6. \(-6x^{6}-108x^{5}-486x^{4}\)
7. \(3p^{4}+12p^{3}+12p^{2}\)
8. \(45a^{21}-20a^{5}\)
9. \(-5q^{4}-80q^{3}-320q^{2}\)
10. \(8b^{16}-98b^{2}\)
11. \(-48s^{11}-24s^{8}-3s^{5}\)
12. \(-27b^{7}+36b^{6}-12b^{5}\)

---

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

Verbetersleutel

1. \(24y^{18}-294y^{4}=6y^{4}(4y^{14}-49)=6y^{4}(2y^7+7)(2y^7-7)\)
2. \(125s^{12}-20s^{2}=5s^{2}(25s^{10}-4)=5s^{2}(5s^5+2)(5s^5-2)\)
3. \(-320p^{7}+560p^{6}-245p^{5}=-5p^{5}(64p^{2}-112p+49)=-5p^{5}(8p-7)^2\)
4. \(-p^{7}+6p^{6}-9p^{5}=-p^{5}(p^2-6p+9)=-p^{5}(p-3)^2\)
5. \(5p^{4}-180p^{2}=5p^{2}(p^2-36)=5p^{2}(p-6)(p+6)\)
6. \(-6x^{6}-108x^{5}-486x^{4}=-6x^{4}(x^2+18x+81)=-6x^{4}(x+9)^2\)
7. \(3p^{4}+12p^{3}+12p^{2}=3p^{2}(p^2+4p+4)=3p^{2}(p+2)^2\)
8. \(45a^{21}-20a^{5}=5a^{5}(9a^{16}-4)=5a^{5}(3a^8+2)(3a^8-2)\)
9. \(-5q^{4}-80q^{3}-320q^{2}=-5q^{2}(q^2+16q+64)=-5q^{2}(q+8)^2\)
10. \(8b^{16}-98b^{2}=2b^{2}(4b^{14}-49)=2b^{2}(2b^7+7)(2b^7-7)\)
11. \(-48s^{11}-24s^{8}-3s^{5}=-3s^{5}(16s^{6}+8s^3+1)=-3s^{5}(4s^3+1)^2\)
12. \(-27b^{7}+36b^{6}-12b^{5}=-3b^{5}(9b^{2}-12b+4)=-3b^{5}(3b-2)^2\)