Câu hỏi của Hoàng Ngân Anh

Question

Phân tích các đa thức sau thành nhân tử:                              A= ( x^2+x)^2 + 4x^2+ 4x -12   ,                                   B=(x^2+ x + 1) (x^2+x + 2) -12     ,...

Khôi Bùi · Accepted Answer

$B=\left(x^2+x+1\right)\left(x^2+x+2\right)-12$

$\Leftrightarrow B=\left(x^2+x+\dfrac{3}{2}-\dfrac{1}{2}\right)\left(x^2+x+\dfrac{3}{2}+\dfrac{1}{2}\right)-12$

$\Leftrightarrow B=\left(x^2+x+\dfrac{3}{2}\right)^2-\dfrac{1}{4}-12$

$\Leftrightarrow B=\left(x^2+x+\dfrac{3}{2}\right)^2-\dfrac{49}{4}$

$\Leftrightarrow B=\left(x^2+x+\dfrac{3}{2}-\dfrac{7}{2}\right)\left(x^2+x+\dfrac{3}{2}+\dfrac{7}{2}\right)$

$\Leftrightarrow B=\left(x^2+x-2\right)\left(x^2+x+5\right)$

$C=x\left(x+1\right)\left(x+2\right)\left(x+3\right)+1$

$\Leftrightarrow C=x\left(x+3\right)\left(x+1\right)\left(x+2\right)+1$

$\Leftrightarrow C=\left(x^2+3x\right)\left(x^2+x+2x+2\right)+1$

$\Leftrightarrow C=\left(x^2+3x\right)\left(x^2+3x+2\right)+1$

$\Leftrightarrow C=\left(x^2+3x+1-1\right)\left(x^2+3x+1+1\right)+1$

$\Leftrightarrow C=\left(x^2+3x+1\right)^2-1+1$

$\Leftrightarrow C=\left(x^2+3x+1\right)^2$

$D=\left(x-1\right)\left(x-3\right)\left(x-5\right)\left(x-7\right)-20$

$\Leftrightarrow D=\left(x-1\right)\left(x-7\right)\left(x-3\right)\left(x-5\right)-20$

$\Leftrightarrow D=\left(x^2-x-7x+7\right)\left(x^2-3x-5x+15\right)-20$

$\Leftrightarrow D=\left(x^2-8x+7\right)\left(x^2-8x+15\right)-20$

$\Leftrightarrow D=\left(x^2-8x+11-4\right)\left(x^2-8x+11+4\right)-20$

$\Leftrightarrow D=\left(x^2-8x+11\right)^2-16-20$

$\Leftrightarrow D=\left(x^2-8x+11\right)^2-36$

$\Leftrightarrow D=\left(x^2-8x+11-6\right)\left(x^2-8x+11+6\right)$

$\Leftrightarrow D=\left(x^2-8x+5\right)\left(x^2-8x+17\right)$

:DCâu trả lời: $B=\left(x^2+x+1\right)\left(x^2+x+2\right)-12$