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\(x^3+5x^2+5x+1\)
\(=\left(x+1\right)\left(x^2+x+1\right)+5x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2+6x+1\right)\)
#)Giải :
\(x^3-2x-4\)
\(=x^3+2x^2-2x^2+2x-4x-4\)
\(=x^3+2x^2+2x-2x^2-4x-4\)
\(=x\left(x^2+2x+2\right)-2\left(x^2+2x+2\right)\)
\(=\left(x-2\right)\left(x^2+2x+2\right)\)
\(x^4+2x^3+5x^2+4x-12\)
\(=x^4+x^3+6x^2+x^3+x^2+6x-2x^2-2x-12\)
\(=x^2\left(x^2+x+6\right)+x\left(x^2+x+6\right)-2\left(x^2+x+6\right)\)
\(=\left(x^2+x+6\right)\left(x^2+x-2\right)\)
\(=\left(x^2+x+6\right)\left(x-1\right)\left(x+2\right)\)
Câu 1.
Đoán được nghiệm là 2.Ta giải như sau:
\(x^3-2x-4\)
\(=x^3-2x^2+2x^2-4x+2x-4\)
\(=x^2\left(x-2\right)+2x\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+2x+2\right)\)
-8x2 + 5x + 3
<=> -8x2 + 8x - 3x + 3
<=> 8x(x - 1) - 3(x - 1)
<=> (8x - 3)(x - 1)
-8x2+5x+3
=−1(8𝑥2−5𝑥−3)
=−1(8𝑥2+3𝑥−8𝑥−3)
=−1(𝑥(8𝑥+3)−1(8𝑥+3))=−1(𝑥−1)(8𝑥+3)\(2x^2+5x+3=2x^2+2x+3x+3=2x\left(x+1\right)+3\left(x+1\right)=\left(2x+3\right)\left(x+1\right)\)
\(2x^2+5x+3=2x^2+2x+3x+3=\left(2x^2+2x\right)+\left(3x+3\right)=2x\left(x+1\right)+3\left(x+1\right)=\left(x+1\right)\left(2x+3\right)\)
\(2x^2+5x-3\\ =2x^2+6x-x-3\\ =2x\left(x+3\right)-\left(x+3\right)\\ =\left(x+3\right)\left(2x-1\right)\)
\(=2x^2-6x+x-3=\left(x-3\right)\left(2x+1\right)\)
\(=2x^2-6x+x-3=2x\left(x-3\right)+\left(x-3\right)=\left(2x+1\right)\left(x-3\right)\)
= 2x^2 - x + 6x - 3
= x(2x - 1) + 3(2x - 1)
= (x + 3)(2x - 1)
\(2x^2+5x-3\)
\(=2x^2+6x-x-3\)
\(=2x\left(x+3\right)-\left(x+3\right)\)
\(=\left(2x-1\right)\left(x+3\right)\)
5x3-40=5(x3-8)=5(x3-23)=5(x-2)(x2+2x+4)
quá đúng rồi