which expression is equivalent to $n^{2}+26n + 88$ for all values of $n$?\n$(n + 8)(n + 11)$\n$(n + 4)(n +…

which expression is equivalent to $n^{2}+26n + 88$ for all values of $n$?\n$(n + 8)(n + 11)$\n$(n + 4)(n + 22)$\n$(n + 4)(n + 24)$\n$(n + 8)(n + 18)$

which expression is equivalent to $n^{2}+26n + 88$ for all values of $n$?\n$(n + 8)(n + 11)$\n$(n + 4)(n + 22)$\n$(n + 4)(n + 24)$\n$(n + 8)(n + 18)$

Answer

Explanation:

Step1: Expand the general - form of factored quadratic

The general form of factoring a quadratic expression (ax^{2}+bx + c) as ((x + m)(x + n)) gives (x^{2}+(m + n)x+mn). For the quadratic (n^{2}+26n + 88), we need to find two numbers (m) and (n) such that (m + n=26) and (mn = 88).

Step2: Check each option

  • Option 1: Expand ((n + 8)(n + 11)) using the FOIL method. ((n + 8)(n + 11)=n^{2}+11n+8n + 88=n^{2}+19n + 88).
  • Option 2: Expand ((n + 4)(n + 22)) using the FOIL method. ((n + 4)(n + 22)=n^{2}+22n+4n + 88=n^{2}+26n + 88).
  • Option 3: Expand ((n + 4)(n + 24)) using the FOIL method. ((n + 4)(n + 24)=n^{2}+24n+4n + 96=n^{2}+28n + 96).
  • Option 4: Expand ((n + 8)(n + 18)) using the FOIL method. ((n + 8)(n + 18)=n^{2}+18n+8n + 144=n^{2}+26n + 144).

Answer:

B. ((n + 4)(n + 22))