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\(x^2+x-6\\ =x^2-2x+3x-6\\ =x\left(x-2\right)+3\left(x-2\right)\\ =\left(x+3\right)\left(x-2\right)\)
Đáp án: B
\(x^2\left(x+1\right)-x\left(x+1\right)\\ =\left(x^2-x\right)\left(x+1\right)\\ =x\left(x-1\right)\left(x+1\right)\)
Vậy: Chọn D.
Ta có: \(x^4+8x\\ =x\left(x^3+8\right)\\ =x\left(x+2\right)\left(x^2-2x+4\right)\)
Vậy: Chọn D
b)x3-7x+6=x3-x-6x+6=x(x2-1)-6(x-1)=x(x-1)(x+1)-6(x-1)
=(x-1)[x(x+1)-6]=(x-1)(x2+x-6)=(x-1)(x2+3x-2x-6)=(x-1)[x(x+3)-2(x+3)]=(x-1)(x-2)(x+3)
c)x3-x2-x-2
=x3-2x2+x2-2x+x-2
=x2(x-2)+x(x-2)+(x-2)
=(x-2)(x2+x+1)
\(x^3-7x+6\)
\(=x^3-x^2+x^2-x-6x+6\)
\(=x^2\left(x-1\right)+x\left(x-1\right)-6\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+x-6\right)\)
\(=\left(x-1\right)\left(x-2\right)\left(x+3\right)\)
a) x2 – 4x + 3 = x2 – x - 3x + 3
= x(x - 1) - 3(x - 1) = (x -1)(x - 3)
b) x2 + 5x + 4 = x2 + 4x + x + 4
= x(x + 4) + (x + 4)
= (x + 4)(x + 1)
c) x2 – x – 6 = x2 +2x – 3x – 6
= x(x + 2) - 3(x + 2)
= (x + 2)(x - 3)
d) x4+ 4 = x4 + 4x2 + 4 – 4x2
= (x2 + 2)2 – (2x)2
= (x2 + 2 – 2x)(x2 + 2 + 2x)
Bài giải:
a) x2 – 4x + 3 = x2 – x - 3x + 3
= x(x - 1) - 3(x - 1) = (x -1)(x - 3)
b) x2 + 5x + 4 = x2 + 4x + x + 4
= x(x + 4) + (x + 4)
= (x + 4)(x + 1)
c) x2 – x – 6 = x2 +2x – 3x – 6
= x(x + 2) - 3(x + 2)
= (x + 2)(x - 3)
d) x4+ 4 = x4 + 4x2 + 4 – 4x2
= (x2 + 2)2 – (2x)2
= (x2 + 2 – 2x)(x2 + 2 + 2x)
Câu 2 nha
\(a,x^4+2x^3+x^2\)
\(=x^2\left(x^2+2x+1\right)\)
\(=x^2\left(x+1\right)^2\)
\(c,x^2-x+3x^2y+3xy^2+y^3-y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)^3-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2+2xy+y^2-1\right)\)
a) \(x^{12}-3x^6+1\)
\(=\left(x^6\right)^2-2\cdot x^6\cdot1+1^2-x^6\)
\(=\left(x^6-1\right)^2-\left(x^3\right)^2\)
\(=\left(x^6-x^3-1\right)\left(x^6+x^3-1\right)\)
b) \(x^4+6x^3+7x^2-6x+1\)
\(=x^4+\left(6x^3-2x^2\right)+\left(9x^2-6x+1\right)\)
\(=\left(x^2\right)^2+2x^2\left(3x-1\right)+\left(3x-1\right)^2\)
\(=\left(x^2+3x-1\right)^2\)
Chọn B.
x 2 + x - 6 = x 2 - 2x+3x- 6 = x(x-2)+3(x - 2) = (x + 3)(x − 2)