How many factors in the expression 8(x+4)(y+4)z^2+4z+7) have exactly two terms
Accepted Solution
A:
The answer is: " 2 {two}" . _________________________________________________________ There are "2 {two}" factors in the expression: _________________________________________________________ → " 8(x + 4)(y + 4)(z² + 4z + 7) " ;
that have "exactly two terms". The factors are: _________________________________________________________ " (x + 4) " ; and: " (y + 4) " . _________________________________________________________ Note: ________________________________________________________ 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" . _________________________________________________________ Explanation: _________________________________________________________ We are given the expression:
" 8(x + 4)(y + 4)(z² + 4z + 7) " ; _________________________________________________________ There are 4 (four) factors in this expression; which are:
1) " 8 " ; 2) "(x + 4)" ; 3) "(y + 4)" ; and: 4) "(z² + 4z + 7)" . _________________________________________________________ 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" . _________________________________________________________
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. ___________________________________________________________