Question

(ii) (2x + 3) (2x + 5)(x - 1)(x - 2) = 30​

Answer 1

Answer:

Step-by-step explanation:

(3 + 2x)(2x + 5)(x + -1)(x + -2) = 30

Reorder the terms:

(3 + 2x)(5 + 2x)(x + -1)(x + -2) = 30

(3 + 2x)(5 + 2x)(-1 + x)(x + -2) = 30

(3 + 2x)(5 + 2x)(-1 + x)(-2 + x) = 30

Multiply (3 + 2x) * (5 + 2x)

(3(5 + 2x) + 2x * (5 + 2x))(-1 + x)(-2 + x) = 30

((5 * 3 + 2x * 3) + 2x * (5 + 2x))(-1 + x)(-2 + x) = 30

((15 + 6x) + 2x * (5 + 2x))(-1 + x)(-2 + x) = 30

(15 + 6x + (5 * 2x + 2x * 2x))(-1 + x)(-2 + x) = 30

(15 + 6x + (10x + 4x2))(-1 + x)(-2 + x) = 30

Combine like terms: 6x + 10x = 16x

(15 + 16x + 4x2)(-1 + x)(-2 + x) = 30

Multiply (15 + 16x + 4x2) * (-1 + x)

(15(-1 + x) + 16x * (-1 + x) + 4x2 * (-1 + x))(-2 + x) = 30

((-1 * 15 + x * 15) + 16x * (-1 + x) + 4x2 * (-1 + x))(-2 + x) = 30

((-15 + 15x) + 16x * (-1 + x) + 4x2 * (-1 + x))(-2 + x) = 30

(-15 + 15x + (-1 * 16x + x * 16x) + 4x2 * (-1 + x))(-2 + x) = 30

(-15 + 15x + (-16x + 16x2) + 4x2 * (-1 + x))(-2 + x) = 30

(-15 + 15x + -16x + 16x2 + (-1 * 4x2 + x * 4x2))(-2 + x) = 30

(-15 + 15x + -16x + 16x2 + (-4x2 + 4x3))(-2 + x) = 30

Combine like terms: 15x + -16x = -1x

(-15 + -1x + 16x2 + -4x2 + 4x3)(-2 + x) = 30

Combine like terms: 16x2 + -4x2 = 12x2

(-15 + -1x + 12x2 + 4x3)(-2 + x) = 30

Multiply (-15 + -1x + 12x2 + 4x3) * (-2 + x)

(-15(-2 + x) + -1x * (-2 + x) + 12x2 * (-2 + x) + 4x3 * (-2 + x)) = 30

((-2 * -15 + x * -15) + -1x * (-2 + x) + 12x2 * (-2 + x) + 4x3 * (-2 + x)) = 30

((30 + -15x) + -1x * (-2 + x) + 12x2 * (-2 + x) + 4x3 * (-2 + x)) = 30

(30 + -15x + (-2 * -1x + x * -1x) + 12x2 * (-2 + x) + 4x3 * (-2 + x)) = 30

(30 + -15x + (2x + -1x2) + 12x2 * (-2 + x) + 4x3 * (-2 + x)) = 30

(30 + -15x + 2x + -1x2 + (-2 * 12x2 + x * 12x2) + 4x3 * (-2 + x)) = 30

(30 + -15x + 2x + -1x2 + (-24x2 + 12x3) + 4x3 * (-2 + x)) = 30

(30 + -15x + 2x + -1x2 + -24x2 + 12x3 + (-2 * 4x3 + x * 4x3)) = 30

(30 + -15x + 2x + -1x2 + -24x2 + 12x3 + (-8x3 + 4x4)) = 30

Combine like terms: -15x + 2x = -13x

(30 + -13x + -1x2 + -24x2 + 12x3 + -8x3 + 4x4) = 30

Combine like terms: -1x2 + -24x2 = -25x2

(30 + -13x + -25x2 + 12x3 + -8x3 + 4x4) = 30

Combine like terms: 12x3 + -8x3 = 4x3

(30 + -13x + -25x2 + 4x3 + 4x4) = 30

Add '-30' to each side of the equation.

30 + -13x + -25x2 + 4x3 + -30 + 4x4 = 30 + -30

30 + -30 + -13x + -25x2 + 4x3 + 4x4 = 30 + -30

Combine like terms: 30 + -30 = 0

0 + -13x + -25x2 + 4x3 + 4x4 = 30 + -30

-13x + -25x2 + 4x3 + 4x4 = 30 + -30

Combine like terms: 30 + -30 = 0

-13x + -25x2 + 4x3 + 4x4 = 0

Solving

-13x + -25x2 + 4x3 + 4x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.

x(-13 + -25x + 4x2 + 4x3) = 0