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

1 answer:

7 0

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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