Question

How many factors in the expression 8(x+4)(y+4)z^2+4z+7) have exactly two terms

Answer 1

The answer is:  " 2 {two}" .
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There are "2 {two}" factors in the expression: 
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          →     " 8(x + 4)(y + 4)(z² + 4z + 7) " ;   

            that have "exactly two terms".  The factors are:
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   " (x + 4) " ;  and:  " (y + 4) " .
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Note:
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    Among the 4 (four) factors; the following 2 (TWO) factors have exactly 2 (two) terms:

    " (x + 4)" ;  →  The 2 (two) terms are "x" and "4" ;   AND:

    " (y + 4)" ;  →  The 2 (two) terms are "y" and "4" .
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Explanation:
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We are given the expression:

            " 8(x + 4)(y + 4)(z² + 4z + 7) " ; 
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There are 4 (four) factors in this expression; which are:

     1)  " 8 "  ;   2)  "(x + 4)" ;  3)  "(y + 4)" ; and:  4)  "(z² + 4z + 7)" .
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     Among the 4 (four) factors; the following factors have exactly 2 (two) terms:

    " (x + 4)" ;  →  The 2 (two) terms are "x" and "4" ;   AND:

    " (y + 4)" ;  →  The 2 (two) terms are "y" and "4" .
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Note:  Let us consider the remaining 2 (two) factors in the given expression:
" 8(x + 4)(y + 4)(z² + 4z + 7) " 

Consider the factor:  " 8 " ;  →  This factor has only one term— " 8 " ;
                          →   { NOT "2 (two) terms" } ; so we can rule out this option.

The last remaining factor is:  " (z² + 4z + 7) " .

       →  This factor has "3 (three) terms" ; which are:
  
1)  " z² " ;  2)  "4z" ; and:  3)  " 7 " ;  

                          →  { NOT "2 (two) terms" } ; so we can rule out this option.
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