Toán Lớp 8: chuyển thành nhân tử. `a, x^4+64` `b, 81x^4+1` `c, x^5+x^4+1` `d, x^7+x^2+1`

Question

Toán Lớp 8:  chuyển thành nhân tử. a, x^4+64 b, 81x^4+1 c, x^5+x^4+1 d, x^7+x^2+1

truongankimtrong · Answer

$a)x^4+64$   $=[(x^2)^2+2.8x^2+8^2]-16x^2$   $=(x^2+8)^2-(4x)^2$   $=(x^2+4x+8)(x^2-4x+8)$   $b)81x^4+1$   $=[(9x^2)^2+2.9x^2+1^2]-18x^2$   $=(9x^2+1)^2-(3 sqrt[]{2})^2$   $=(9x^2+3 sqrt[]{2}+1)(9x^2-3 sqrt[]{2}+1)$   $c)x^5+x^4+1$   $=x^5+x^4+x^3-x^3+1$   $=x^3(x^2+x+1)-(x^3-1)$   $=x^3(x^2+x+1)-(x-1)(x^2+x+1)$   $=(x^2+x+1)(x^3-x+1)$   $d)x^7+x^2+1$   $=x^7+x^6-x^6+x^5-x^5+x^4-x^4+x^3-x^3+x^2+1$   $=x^5(x^2+x+1)-x^4(x^2+x+1)+x^2(x^2+x+1)-(x^3-1)$   $=(x^2+x+1)(x^5-x^4+x^2)-(x-1)(x^2+x+1)$   $=(x^2+x+1)(x^5-x^4+x^2-x+1)$

cattien · Answer

a. x^4+64   =(x^4+16x^2+64)-16x^2   =(x^2+8)-(4x)^2   =(x^2+4x+8)(x^2-4x+8)   b. 81x^4+1   =(81x^4+18x^2+1)-18x^2   =(9x^2+1)^2-(3 sqrt{2}x)^2   =(9x^2+3 sqrt{2}x+1)(9x^2-3 sqrt{2}x+1)   c. x^5+x^4+1   =(x^5+x^4+x^3)-(x^3-1)   =x^3(x^2+x+1)-(x-1)(x^2+x+1)   =(x^3-x+1)(x^2+x+1)   d. x^7+x^2+1   =(x^7+x^6+x^5)-(x^6+x^5+x^4)+(x^4+x^3+x^2)-(x^3-1)   =x^5(x^2+x+1)-x^4(x^2+x+1)+x^2(x^2+x+1)-(x-1)(x^2+x+1)   =(x^5-x^4+x^2-x+1)(x^2+x+1).