What is the binomials is a factor of the trinomials x^2+13x+40? a. x-5 b. x+5 c. x+4 d. x-4

The correct answer is:   [B]:    " (x + 5) " .

Explanation:

To solve:

Given:

" x²  +  13x + 40 " ;  factor into "two terms" ;

    →  that is;    "factor into 2 (two) binomial expressions" .

  What 2 (two) factors of:  "+ 40"  add up to " + 13 " ?  ;

+ 40, + 1  ?? ;  →   +40 + (+1) = +41 ;  →  + 41 ≠  + 13 ;

 - 40 + (-1) ?? ;  →  - 40 + (-1) = - 40 - 1 = - 41 ;  →  - 41  ≠ +13 ;

  +8, + 5 ?? ;     →  + 8 + 5 = + 13 ;  →  + 13  = + 13 .  Yes!

So;  the factors of:  " x²  +  13x + 40 "  ;

are:  " (x + 5) (x + 8) " .

        Among this 2 (two) binomial factors:  "(x + 5)"  AND:  "(x + 8)" ;

  one of these:  " (x + 5) "   —   appears among the answer choices provided;

        →  which is:     [B]:    " (x + 5) " .

The correct answer is:    [B]:     " (x + 5) " .

Hope this helps!

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     within the community!