Question

phân tích đa thức thành nhân tử : x^8+98x^4+1.

giúp suli các bn nha ,,,

Answer 1

\(x^8+98x^4+1\)

\(=\left(x^8+2x^4+1\right)+96x^4\)

\(=\left(x^4+1\right)^2+16\left(x^4+1\right)x^2+64x^4-16\left(x^4+1\right)x^2+32x^4\)

\(=\left(x^4+1+8x^2\right)^2-16x^2\left(x^4+1-2x^2\right)\)

\(=\left(x^4+8x^2+1\right)^2-\left[4x\left(x^2-1\right)\right]^2\)

\(=\left(x^4+8x^2+1-4x^3+4x\right)\left(x^4+8x^2+1+4x^3-4x\right)\)

Answer 2

x⁸ + 98x⁴ + 1

= (x⁸ + 2x⁴ + 1 ) + 96x⁴

= (x⁴ + 1)² + 16x²(x4 + 1) + 64x⁴ - 16x²(x⁴ + 1) + 32x⁴

= (x⁴ + 1 + 8x²)² – 16x²(x⁴ + 1 – 2x²)

= (x⁴ + 8x² + 1)² - 16x²(x² – 1)²

= (x⁴ + 8x² + 1)² - (4x³ – 4x )²

= (x⁴ + 4x³ + 8x² – 4x + 1)(x⁴ - 4x³ + 8x² + 4x + 1)

Answer 3

x8 + 98x4 + 1 = (x8 + 2x4 + 1 ) + 96x4
= (x4 + 1)2 + 16x2(x4 + 1) + 64x4 - 16x2(x4 + 1) + 32x4
= (x4 + 1 + 8x2)2 – 16x2(x4 + 1 – 2x2) = (x4 + 8x2 + 1)2 - 16x2(x2 – 1)2
= (x4 + 8x2 + 1)2 - (4x3 – 4x )2
= (x4 + 4x3 + 8x2 – 4x + 1)(x4 - 4x3 + 8x2 + 4x + 1)