which of the following expressions is equivalent to $x^{2}-x - 30$?\na. $(x + 3)(x - 10)$\nb. $(x + 6)(x…

which of the following expressions is equivalent to $x^{2}-x - 30$?\na. $(x + 3)(x - 10)$\nb. $(x + 6)(x - 5)$\nc. $(x - 6)(x + 5)$\nd. $(x - 15)(x - 15)$

which of the following expressions is equivalent to $x^{2}-x - 30$?\na. $(x + 3)(x - 10)$\nb. $(x + 6)(x - 5)$\nc. $(x - 6)(x + 5)$\nd. $(x - 15)(x - 15)$

Answer

Explanation:

Step1: Expand each option

  • Option A: $$(x + 3)(x - 10)=x^{2}-10x+3x - 30=x^{2}-7x - 30$$
  • Option B: $$(x + 6)(x - 5)=x^{2}-5x+6x - 30=x^{2}+x - 30$$
  • Option C: $$(x - 6)(x + 5)=x^{2}+5x-6x - 30=x^{2}-x - 30$$
  • Option D: $$(x - 15)(x - 15)=x^{2}-15x-15x + 225=x^{2}-30x + 225$$

Answer:

C. ((x - 6)(x + 5))