Question

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

Answer 1

Only 2 factors have exactly two terms i.e, (x+4)(y+4)

Explanation:

Given : Expression
`8(x+4)(y+4)(z^2+4z+7)`

To find : How many factors in the expression have exactly two terms?

Solution :

Expression
`8(x+4)(y+4)(z^2+4z+7)` cannot be further factorized.

Now, We count the terms in each factor.

1) Factor- 8

Only 1 term i.e, 8 itself.

2) Factor- x+4

Two terms .i.e., x and 4

3) Factor- y+4

Two terms .i.e., y and 4

4) Factor-
`z^2+4z+7`

Three terms .i.e.,
`z^2`, 4z and 7.

Therefore, Only 2 factors have exactly two terms i.e, (x+4)(y+4).

Answer 2

From the expression 8(x +4) (y +4) (z 2 + 4z + 7),
the factors are 8, (x+4), (y+4), (z^2 + 4z + 7) since each of these factors, when you divide that to the whole expression won't give a remainder.