which expression is equivalent to $6x^{2}-19x - 55$?\n$(2x - 11)(3x + 5)$\n$(2x + 11)(3x - 5)$\n$(6x - 11)(x…
which expression is equivalent to $6x^{2}-19x - 55$?\n$(2x - 11)(3x + 5)$\n$(2x + 11)(3x - 5)$\n$(6x - 11)(x + 5)$\n$(6x + 11)(x - 5)$
Answer
Explanation:
Step1: Expand the first option
[ \begin{align*} (2x - 11)(3x+5)&=2x\times(3x + 5)-11\times(3x + 5)\ &=6x^{2}+10x-33x - 55\ &=6x^{2}-23x - 55 \end{align*} ]
Step2: Expand the second option
[ \begin{align*} (2x + 11)(3x-5)&=2x\times(3x - 5)+11\times(3x - 5)\ &=6x^{2}-10x+33x - 55\ &=6x^{2}+23x - 55 \end{align*} ]
Step3: Expand the third option
[ \begin{align*} (6x - 11)(x + 5)&=6x\times(x + 5)-11\times(x + 5)\ &=6x^{2}+30x-11x - 55\ &=6x^{2}+19x - 55 \end{align*} ]
Step4: Expand the fourth option
[ \begin{align*} (6x + 11)(x - 5)&=6x\times(x - 5)+11\times(x - 5)\ &=6x^{2}-30x+11x - 55\ &=6x^{2}-19x - 55 \end{align*} ]
Answer:
D. $(6x + 11)(x - 5)$