Phân tích đa thức thành nhân tử a) 4x^2 + 4x - 3 b) 4x^2 - 12x - 7

Giúp em giải toán 8 với ạ 😢

Hướng dẫn giải

a) 4x² + 4x - 3 = 4x² + 6x – 2x – 3 = 2x(2x + 3) – (2x + 3) = (2x – 1)(2x + 3)

b) 4x² – 12x – 7 = 4x² – 14x + 2x – 7 = 2x(2x – 7) + (2x – 7) = (2x + 1)(2x – 7)

c) 2x² + x – 6 = 2x² + 4x – 3x – 6 = 2x(x + 2) – 3(x + 2) = (2x – 3)(x + 2)

d) 3x² – 11x + 6 = 3x² – 9x – 2x + 6 = 3x(x – 3) – 2(x – 3) = (3x – 2)(x – 3)

e) 4x² + 16x – 9 = 4x² – 2x + 18x – 9 = 2x(2x – 1) + 9(2x – 1) = (2x + 9)(2x – 1)

f) 6x² + 7x + 2 = 6x² + 3x + 4x + 2 = 3x(2x + 1) + 2(2x + 1) = x(3x + 2)(2x + 1)

g) -5x² – 29x – 20 = -5x² – 25x – 4x – 20 = -5x(x + 5) – 4(x + 5) = (-5x – 4)(x + 5)

h) -7x² + 11x + 6 = -7x² + 14x – 3x + 6 = -7x(x – 2) – 3(x – 2) = (-7x – 3)(x – 2)

k) x² + 2x – 3 = x² + 3x – x – 3= x(x + 3) – (x + 3) = (x – 1)(x + 3)

l) -x² – 4x – 3 = -x² – 3x – x – 3 = -x(x + 3) – (x + 3) = (-x – 1)(x + 3)

m) -x² + 3x – 2 = -x² + 2x + x – 2 = x(x – 2) + (x – 2) = (x + 1)(x – 2)

n) -x² + 25x – 150 = x² + 10x + 15x – 150 = -x(x - 10) + 15(x – 10) = (-x + 15)(x -10)

Bài 41;

a) 15x³ + 7x² – 2x = x(15x² + 7x – 2) = x(15x² + 10x – 3x - 2) = x[5x(3x + 2) – (3x + 2)] = x[(5x – 1)(3x + 2)]

b) 12x⁴ + 7x³ – 12x² = x² (12x² + 7x – 12) = x² [12x² + 16x – 9x – 12] = x²[4x(3x + 4) – 3(3x + 4)] = x² [(4x – 3)(3x + 4)