Phân tích đa thức sau thành nhân tử
a, x^2-6x+5
b, x^2-x-12
c, x^2+8x+15
d,x^2+2xy+y^2+2x+2y-15
e, x^2 +2xy+y^2-x-y-12
g, 3x^2+13x-10
f, 64x^4+y^4
i, 2x^2-5x-12
Phân tích đa thức sau thành nhân tử
a, x^2-6x+5
b, x^2-x-12
c, x^2+8x+15
d,x^2+2xy+y^2+2x+2y-15
e, x^2 +2xy+y^2-x-y-12
g, 3x^2+13x-10
f, 64x^4+y^4
i, 2x^2-5x-12
a, x²-6x+5
= x² – x – 5x + 5
= (x² – x) – (5x – 5)
= x(x-1) – 5(x – 1)
= (x-1)(x-5)
b, x²-x-12
= x² + 3x – 4x – 12
= x(x+3) – 4(x+3)
= (x+3)(x-4)
c, x²+8x+15
= x² + 3x + 5x +15
= x(x+3) + 5(x+3)
=(x+3)(x+5)
d,x²+2xy+y²+2x+2y-15
= (x²+2xy+y²)+(2x+2y)-15
= (x+y)² + 2(x+y) – 15
= (x+y)² – 3(x+y) + 5(x+y) – 15
= (x+y)(x+y-3) + 5(x+y-3)
= (x+y-3)(x+y+5)
e, x² +2xy+y²-x-y-12
= (x² +2xy+y²)-(x+y)-12
= (x+y)² – (x+y) – 12
= (x+y)² + 3(x+y) – 4(x+y) – 12
= (x+y)(x+y+3) – 4(x+y+3)
=(x+y+3)(x+y-4)
g, 3x²+13x-10
= 3x² + 15x – 2x – 10
= 3x(x+5) – 2(x+5)
= (x+5)(3x-2)
f, 64x^4+y^4
= 64x^4 + 16x²y² – 16x²y² + y^4
= (64x^4 + 16x²y² + y^4) – 16x²y²
= (8x² + y²)² – (4xy)²
= (8x²+y²-4xy)(8x²+y²+4xy)
i, 2x²-5x-12
= 2x² – 8x + 3x – 12
= 2x(x-4) + 3(x-4)
= (x-4)(2x+3)
Đáp án:
Giải thích các bước giải:
\(a,\ x^{2}-6x+5\\ =x^{2}-x-5x-5\\ =(x^{2}-x)-(5x-5)\\ =x(x-1)-5(x-1)\\ =(x-5)(x-1)\\ b,\ x^{2}-x-12\\ =x^{2}+4x-3x-12\\ =(x^{2}+4x)-(3x+12)\\ =x(x+4)-3(x+4)\\ =(x-3)(x+4)\\ c,\ x^{2}+8x+15\\ =x^{2}+3x+5x+15\\ =(x^{2}+3x)+(5x+15)\\ =x(x+3)+5(x+3)\\ =(x+5)(x+3)\\ d,\ x^{2}+2xy+y^{2}+2x+2y-15\\ =(x^{2}+2xy+y^{2})+(2x+2y)-15\\ =(x+y)^{2}+2(x+y)-15\\ =(x+y)^{2}-3(x+y)+5(x+y)-15\\ =(x+y)(x+y-3)+5(x+y-3)\\ =(x+y-3)(x+y+5)\\ e,\ x^{2}+2xy+y^{2}-x-y-12\\ =(x^{2}+2xy+y^{2})-(x+y)-12\\ =(x+y)^{2}-(x+y)-12\\ =(x+y)^{2}-4(x+y)+3(x+y)-12\\ =(x+y)(x+y-4)+3(x+y-4)\\ =(x+y-4)(x+y+3)\\ g,\ 3x^{2}+13x-10\\ =3x^{2}+15x-2x-10\\ =(3x^{2}+15x)-(2x+10)\\ =3x(x+5)-2(x+5)\\ =(3x-2)(x+5)\\ f,\ 64x^{4}+y^{4}\\ =64x^{4}+(16x^{2}y^{2}-16x^{2}y^{2})+y^{4}\\ =64x^{4}+16x^{2}y^{2}+y^{4}-16x^{2}y^{2}\\ =(64x^{4}+16x^{2}y^{2}+y^{4})-(4xy)^{2}\\ =(8x^{2}+y^{2})^{2}-(4xy)^{2}\\ =(8x^{2}+y^{2}-4xy)(8x^{2}+y^{2}+4xy)\\ i,\ 2x^{2}-5x-12\\ =2x^{2}+3x-8x-12\\ =(2x^{2}+3x)-(8x+12)\\ =x(2x+3)-4(2x+3)\\ =(x-4)(2x+3)\)
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