Toán Lớp 8: Phân tích đa thức thành nhân tử.
5. $x^{7}+x^{2}+1$
6. $x^{8}+x^{7}+1$
7. $x^{7}+x^{5}+1$
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Toán Lớp 8: Phân tích đa thức thành nhân tử.
5. $x^{7}+x^{2}+1$
6. $x^{8}+x^{7}+1$
7. $x^{7}+x^{5}+1$
Comments ( 1 )
$\text{ @HV }$
a) x^7 + x^2 + 1
= x^7 + x^6 + x^5 – x^6 – x^5 – x^4 + x^4 + x^3 + x^2 – x^3 – x^2 – x + x^2 + x + 1
= (x^7 + x^6 + x^5) – (x^6 + x^5 + x^4) + (x^4 + x^3 + x^2) – (x^3 + x^2 + x) + (x^2 + x + 1)
= x^5. (x^2 + x + 1) – x^4. (x^2 + x + 1) + x^2. (x^2 + x + 1) – x. (x^2 + x + 1) + 1. (x^2 + x + 1)
= (x^5 – x^4 + x^2 – x + 1). (x^2 + x + 1)
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b) x^8 + x^7 + 1
= x^8 + x^7 – x^6 + x^6 + 1
= (x^8 + x^7 + x^6) – [(x^3)^2 – 1]
= x^6. (x^2 + x + 1) – (x^3 – 1). (x^3 + 1)
= x^6. (x^2 + x + 1) – (x – 1). (x^2 + x + 1). (x^3 + 1)
= (x^2 + x + 1). [x^6 – (x – 1). (x^3 + 1)]
= (x^2 + x + 1). [x^6 – (x^4 + x – x^3 – 1)]
= (x^2 + x + 1). (x^6 – x^4 – x + x^3 + 1)
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c) x^7 + x^5 + 1
= x^7 + x^6 + x^5 – x^6 + 1
= (x^7 + x^6 + x^5) – [(x^3)^2 – 1]
= x^5. (x^2 + x + 1) – (x^3 – 1). (x^3 + 1)
= x^5. (x^2 + x + 1) – (x – 1). (x^2 + x + 1). (x^3 + 1)
= (x^2 + x + 1). [x^5 – (x – 1). (x^3 + 1)]
= (x^2 + x + 1). [x^5 – (x^4 + x – x^3 – 1)]
= (x^2 + x + 1). (x^5 – x^4 – x + x^3 + 1)