Câu hỏi của ytr

Question

BÀi 1: Phân tích đa thức thành nhân tử

a)x3+8x2+17x+10

b)abc+ab+bc+ca+a+b+c+1

c)4x4+81

d)64x4+y4

e)x5+x4+1

f)x+2y-xy-2

g)a2+b2-x2-y2+2ab-2xy

svtkvtm · Accepted Answer

$a^2+2ab+b^2-x^2-2xy-y^2=\left(a+b\right)^2-\left(x+y\right)^2=\left(a+b+x+y\right)\left(a+b-x-y\right)$$x+2y-xy-2=x-xy+2y-2=x\left(1-y\right)-2\left(1-y\right)=\left(x-2\right)\left(1-y\right)$

$x^5+x^4+1=x^5-x^2+x^4-x+\left(x^2+x+1\right)=x^2\left(x^3-1\right)+x\left(x^3-1\right)+\left(x^2+x+1\right)=x^2\left(x-1\right)\left(x^2+x+1\right)+x\left(x-1\right)\left(x^2+x+1\right)+\left(x^2+x+1\right)=\left(x^2+x+1\right)\left(x^3-x+1\right)$$64x^4+y^4=64x^4+16x^2y^2+y^4-16x^2y^2=\left(8x^2+y^2\right)^2-\left(4xy\right)^2=\left(8x^2-4xy+y^2\right)\left(8x^2+4xy+y^2\right)$Câu trả lời: $a^2+2ab+b^2-x^2-2xy-y^2=\left(a+b\right)^2-\left(x+y\right)^2=\left(a+b+x+y\right)\left(a+b-x-y\right)$$x+2y-xy-2=x-xy+2y-2=x\left(1-y\right)-2\left(1-y\right)=\left(x-2\right)\left(1-y\right)$

$x^5+x^4+1=x^5-x^2+x^4-x+\left(x^2+x+1\right)=x^2\left(x^3-1\right)+x\left(x^3-1\right)+\left(x^2+x+1\right)=x^2\left(x-1\right)\left(x^2+x+1\right)+x\left(x-1\right)\left(x^2+x+1\right)+\left(x^2+x+1\right)=\left(x^2+x+1\right)\left(x^3-x+1\right)$$64x^4+y^4=64x^4+16x^2y^2+y^4-16x^2y^2=\left(8x^2+y^2\right)^2-\left(4xy\right)^2=\left(8x^2-4xy+y^2\right)\left(8x^2+4xy+y^2\right)$

svtkvtm · Answer

$x^3+8x^2+17x+10=\left(x^3+2x^2\right)+\left(6x^2+12x\right)+\left(5x+10\right)=x^2\left(x+2\right)+6x\left(x+2\right)+5\left(x+2\right)=\left(x^2+6x+5\right)\left(x+2\right)=\left(x+1\right)\left(x+2\right)\left(x+5\right)$ $4x^4+81=4x^4+36x^2+81-36x^2=\left(2x^2+9\right)^2-\left(6x\right)^2=\left(2x^2+6x+9\right)\left(2x^2-6x+9\right)$$abc+ab+bc+ca+a+b+c+1=\left(abc+ab\right)+\left(bc+b\right)+\left(ca+a\right)+\left(c+1\right)=ab\left(c+1\right)+b\left(c+1\right)+a\left(c+1\right)+\left(c+1\right)=\left(c+1\right)\left(ab+a+b+1\right)=\left(c+1\right)\left(a+1\right)\left(b+1\right)$Câu trả lời: $x^3+8x^2+17x+10=\left(x^3+2x^2\right)+\left(6x^2+12x\right)+\left(5x+10\right)=x^2\left(x+2\right)+6x\left(x+2\right)+5\left(x+2\right)=\left(x^2+6x+5\right)\left(x+2\right)=\left(x+1\right)\left(x+2\right)\left(x+5\right)$ $4x^4+81=4x^4+36x^2+81-36x^2=\left(2x^2+9\right)^2-\left(6x\right)^2=\left(2x^2+6x+9\right)\left(2x^2-6x+9\right)$$abc+ab+bc+ca+a+b+c+1=\left(abc+ab\right)+\left(bc+b\right)+\left(ca+a\right)+\left(c+1\right)=ab\left(c+1\right)+b\left(c+1\right)+a\left(c+1\right)+\left(c+1\right)=\left(c+1\right)\left(ab+a+b+1\right)=\left(c+1\right)\left(a+1\right)\left(b+1\right)$

Minh Anh · Answer

a) x3 + x2 + 7x2 + 10x + 7x + 10

= x2(x+1) + 7x(x+1) + 10(x+1)

= (x+1)(x2 + 7x + 10)

b) abc + ab + bc + ca + a + b + c + 1

=(abc + bc) + (ab + a) + (ca + c) + (a + 1)

= bc(a + 1) + a(b+1) + c(a + 1) + 1(a+1)

= (a + 1)(bc + a + c + 1)

c) 4x4 + 81

= 4x4 + 36x2 + 81 - 36x2

= (2x2)2 + 2.2x2.9 + 92 - (6x)2

= (2x2 + 9)2 - (6x)2 (áp dụng hằng đẳng thức đáng nhớ số 1)

= (2x2 + 9 - 6x)(2x2 + 9 + 6x) (áp dụng hằng đẳng thức đáng nhớ số 3)

d) 64x4 + y4

= 64x4 + 16x2y2 + y4 - 16x2y2

= (8x2)2 + 2.8x2.y2 + (y2)2 - (4xy)2

= (8x2 + y2)2 - (4xy)2 (áp dụng hằng đẳng thức đáng nhớ sô 1)

= (8x2 + y2 - 4xy)(8x2 + y2 + 4xy) (áp dụng hằng đẳng thức đáng nhớ số 3)

e) x5 + x4 + 1

= x5 - x2 + (x4 + x2 + 1)

= x2(x3 - 1) + (x4 + x2 + 1)

= x2(x-1)(x2 + x + 1) + (x4 + 2x2 + 1 - x2) (áp dụng hằng đẳng thức số 7)

= (x3 - 1)(x2 + x + 1) + [(x2)2 + 2.x2.1 + 12 - x2 ]

= (x3 - 1)(x2 + x + 1) + [(x2 + 1)2 - x2 ] (áp dụng hằng đẳng thức số 1)

= (x3 - 1)(x2 + x + 1) + (x2 + 1 - x2)(x2 + 1 + x2) ( áp dụng hằng đẳng thức số 3)

= (x2 + x + 1)(x3 - 1 + x2 - x + 1)

= (x2 + x + 1)(x3 + x2 - x)

Đơi làm nốt, đang oải lắm!Câu trả lời: a) x3 + x2 + 7x2 + 10x + 7x + 10