Phân tích thành nhân tử
a) \(\left(2x^2-x-1\right)\left(2x^2-x-4\right)-10\)
b) \(\left(5x^2-2x\right)^2+2x-5x^2-6\)
c) \(\left(x^2+5x\right)^2+10x^2+5x+24\)
d) \(\left(x^2+x-2\right)\left(x^2+9x+18\right)-28\)
e) \(\left(x^2+8x+12\right)\left(x^2+12x+32\right)+16\)
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Phân tích thành nhân tử
a) \(\left(2x^2-x-1\right)\left(2x^2-x-4\right)-10\)
b) \(\left(5x^2-2x\right)^2+2x-5x^2-6\)
c) \(\left(x^2+5x\right)^2+10x^2+5x+24\)
d) \(\left(x^2+x-2\right)\left(x^2+9x+18\right)-28\)
e) \(\left(x^2+8x+12\right)\left(x^2+12x+32\right)+16\)
a: \(=\left(2x^2-x\right)^2-5\left(2x^2-x\right)-6\)
\(=\left(2x^2-x\right)^2-6\left(2x^2-x\right)+\left(2x^2-x-6\right)\)
\(=\left(2x^2-x-6\right)\left(2x^2-x+1\right)\)
\(=\left(2x^2-4x+3x-6\right)\left(2x^2-x+1\right)\)
\(=\left(x-2\right)\left(2x+3\right)\left(2x^2-x+1\right)\)
b: \(=\left(5x^2-2x\right)^2-\left(5x^2-2x\right)-6\)
\(=\left(5x^2-2x-6\right)\left(5x^2-2x+1\right)\)
d: \(=\left(x+2\right)\left(x-1\right)\left(x+3\right)\left(x+6\right)-28\)
\(=\left(x^2+5x+6\right)\left(x^2+5x-6\right)-28\)
\(=\left(x^2+5x\right)^2-36-28\)
\(=\left(x^2+5x\right)^2-64\)
\(=\left(x^2+5x+8\right)\left(x^2+5x-8\right)\)