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 each option

For option A: \((2x - 11)(3x + 5)\)
Using the distributive property (FOIL method):
\(2x\times3x + 2x\times5 - 11\times3x - 11\times5\)
\(= 6x^{2}+10x - 33x - 55\)
\(= 6x^{2}-23x - 55\) (Not equivalent)

Step2: Expand option B

\((2x + 11)(3x - 5)\)
\(2x\times3x + 2x\times(-5)+11\times3x + 11\times(-5)\)
\(= 6x^{2}-10x + 33x - 55\)
\(= 6x^{2}+23x - 55\) (Not equivalent)

Step3: Expand option C

\((6x - 11)(x + 5)\)
\(6x\times x + 6x\times5 - 11\times x - 11\times5\)
\(= 6x^{2}+30x - 11x - 55\)
\(= 6x^{2}+19x - 55\) (Not equivalent)

Step4: Expand option D

\((6x + 11)(x - 5)\)
\(6x\times x + 6x\times(-5)+11\times x + 11\times(-5)\)
\(= 6x^{2}-30x + 11x - 55\)
\(= 6x^{2}-19x - 55\) (Equivalent)

Answer:

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