Question

Phân tích đa thức thành nhân tử:

a) x^2+10x+25-y^2

b) 5x^3-7x^2+10x-14

c) -5y^2+30y-45

e) 4xy^2-8xyz+4xz^2

f) x^2+7x+10

k) 2x^7+6x^6+6x^5-2x^4

 

Answer 1

a)\(x^2+10x+25-y^2\)

\(=\left(x+5\right)^2-y^2\)

\(=\left(x+5+y\right)\left(x+5-y\right)\)

b)\(5x^3-7x^2+10x-14\)

\(=x^2\left(5x-7\right)+2\left(5x-7\right)\)

\(=\left(x^2+2\right)\left(5x-7\right)\)

c)\(-5y^2+30y-45\)

\(=-5\left(y^2-6y+9\right)\)

\(=-5\left(y-3\right)^2\)

e)\(4xy^2-8xyz+4xz^2\)

\(=4x\left(y^2-2yz+z^2\right)\)

\(=4x\left(y-z\right)^2\)

f)\(x^2+7x+10\)

\(=x^2+5x+2x+10\)

\(=x\left(x+5\right)+2\left(x+5\right)\)

\(=\left(x+2\right)\left(x+5\right)\)

k)\(2x^7+6x^6+6x^5-2x^4\)

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

Answer 2

a)\(x^2+10x+25-y^2\)

\(=\left(x+5\right)^2-y^2\)

\(=\left(x+5-y\right)\left(x+5+y\right)\)

b)\(5x^3-7x^2+10x-14\)

\(=x^2\left(5x-7\right)+2\left(5x-7\right)\)

\(=\left(5x-7\right)\left(x^2+2\right)\)

c)\(-5y^2+30y-45\)

\(=-5\left(y^2-6y+9\right)\)

\(=-5\left(y-3\right)^2\)

e)\(4xy^2-8xyz+4xz^2\)

\(=4x\left(y^2-2yz+z^2\right)\)

\(=4x\left(y-z\right)^2\)

f)\(x^2+7x+10\)

\(=x^2+5x+2x+10\)

\(=x\left(x+5\right)+2\left(x+5\right)\)

k)\(2x^7+6x^6+6x^5-2x^4\)

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

\(=\left(x+2\right)\left(x+5\right)\)

 

Answer 3

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