Question

which expression is equivalent to $6x^2 - 19x - 55$?

• $(2x - 11)(3x + 5)$
• $(2x + 11)(3x - 5)$
• $(6x - 11)(x + 5)$
• $(6x + 11)(x - 5)$

Explanation:

Step1: Expand Option 1

Expand \((2x - 11)(3x + 5)\) using FOIL method: \(2x\times3x + 2x\times5 - 11\times3x - 11\times5 = 6x^2 + 10x - 33x - 55 = 6x^2 - 23x - 55\). Not equal to \(6x^2 - 19x - 55\).

Step2: Expand Option 2

Expand \((2x + 11)(3x - 5)\): \(2x\times3x + 2x\times(-5) + 11\times3x + 11\times(-5) = 6x^2 - 10x + 33x - 55 = 6x^2 + 23x - 55\). Not equal.

Step3: Expand Option 3

Expand \((6x - 11)(x + 5)\): \(6x\times x + 6x\times5 - 11\times x - 11\times5 = 6x^2 + 30x - 11x - 55 = 6x^2 + 19x - 55\). Not equal.

Step4: Expand Option 4

Expand \((6x + 11)(x - 5)\): \(6x\times x + 6x\times(-5) + 11\times x + 11\times(-5) = 6x^2 - 30x + 11x - 55 = 6x^2 - 19x - 55\). Matches the given expression.

Answer:

D. \((6x + 11)(x - 5)\)