Phân tích đa thức thành nhân tử:
a) $21 + 2x – 8x^2$
b) $ 6x^2 – 11x – 10$
c) $x^3 – 5x^2 + 8x – 4$
d) $ 4x^2- 8x – 5$
e) $x^2 + 2(a+b)x + 4ab$
f) $4x^2-4x-3$
Phân tích đa thức thành nhân tử:
a) $21 + 2x – 8x^2$
b) $ 6x^2 – 11x – 10$
c) $x^3 – 5x^2 + 8x – 4$
d) $ 4x^2- 8x – 5$
e) $x^2 + 2(a+b)x + 4ab$
f) $4x^2-4x-3$
Đáp án:
a, 21 + 2x – 8x²
= -8x² + 14x – 12x + 21
= -2x(4x – 7) – 3(4x – 7)
=(4x – 7)(-2x – 3)
b, 6x² – 11x -10
=6x² – 15x + 4x – 10
=3x(2x – 5)+2(2x – 5)
=(2x – 5)(3x + 2)
c, x³ – 5x² + 8x – 4
=x³ – x² – 4x² + 4x + 4x -4
=x²(x – 1) – 4x(x – 1) + 4(x – 1)
=(x – 1)(x² – 4x + 4)
=(x – 1)(x – 2)²
d, 4x² – 8x – 5
= 4x² + 2x – 10x – 5
=2x(2x + 1) – 5(2x + 1)
=(2x + 1)(2x – 5)
e, x² + 2(a + b)x + 4ab
=x² + 2ax + 2bx + 4ab
=x(x + 2a) + 2b( x + 2a)
=(x + 2a)(x + 2b)
f, 4x² – 4x – 3
=4x² + 2x – 6x – 3
=2x(2x + 1) – 3(2x + 1)
=(2x + 1)(2x -3)
Đáp án:
Giải thích các bước giải:
$a)21+2x-8x^2$
$=21+14x-12x-8x^2$
$=7(3+2x)-4x(3+2x)$
$=(2x+3)(7-4x)$
$b)6x^2-11x-10$
$=6x^2-15x+4x-10$
$=3x(2x-5)+2(2x-5)$
$=(3x+2)(2x-5)$
$c)x^3-5x^2+8x-4$
$=x^3-x^2-4x^2+4x+4x-4$
$=x^2(x-1)-4x(x-1)+4(x-1)$
$=(x-1)(x^2-4x+4)$
$=(x-1)(x-2)^2$
$d)4x^2-8x-5$
$=4x^2-10x+2x-5$
$=2x(2x-5)+(2x-5)$
$=(2x+1)(2x-5)$
$e)x^2+2(a+b)x+4ab$
$=x^2+2ax+2bx+4ab$
$=x(x+2a)+2b(x+2a)$
$=(x+2a)(x+2b)$
$f)4x^2-4x-3$
$=4x^2-6x+2x-3$
$=2x(2x-3)+(2x-3)$
$=(2x-3)(2x+1)$