Question

phân tích đa thức thành nhân tử

x^4+16

16x^4+1

Answer 1

x⁴+16

=(x²)² +4²

=(x²+4)(x²-4)

16x⁴+1

=(4x²)² +1

=(4x²+1)(4x²-1)

Answer 2

a) \(x^4+16\)

\(=\left(x^2\right)^2+4^2\)

\(=\left(x^2\right)^2+2x^2.4+4^2-2x^2.4\)

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

\(=\left(x^2+4\right)^2-\left(2\sqrt{2}x\right)^2\)

\(=\left(x^2+4-2\sqrt{2}x\right)\left(x^2+4+2\sqrt{2}x\right)\)

b) \(16x^4+1\)

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

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

\(=\left(4x^2\right)^2+2.4x^2+1-2.4x^2\)

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

\(=\left(4x^2+1\right)^2-\left(2\sqrt{2}x\right)^2\)

\(=\left(4x^2+1-2\sqrt{2}x\right)\left(4x^2+1+2\sqrt{2}x\right)\)