Which of the following is a factor of 3xy + 3y - 5x - 5?
x + 1, x² + x + 1, x² + 2x + 1, None of the above

Solution:

Given, the equation 3xy + 3y - 5x - 5.

By grouping, we get,

(3xy + 3y) + (-5x - 5)

By factoring (3xy + 3y),

= 3y(x + 1)

By factoring (-5x - 5),

= -5(x + 1)

By using distributive property, factor out common term (x + 1)

= (x + 1)(3y - 5)

Therefore,the factor is (x + 1)(3y - 5).

Example:

Which of the following is a factor of 2xy + 2y - 6x - 6?

Solution:

Given, the equation 2xy + 2y - 6x - 6.

By grouping, we get,

(2xy + 2y) + (-6x - 6)

By factoring (2xy + 2y),

= 2y(x + 1)

By factoring (-6x - 6),

= -6(x + 1)

By using distributive property, factor out common term (x + 1)

= (x + 1)(2y - 6)

Therefore,the factor is (x + 1)(2y - 6).

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Which of the following is a factor of 3xy + 3y - 5x - 5?

Summary:

The factor of 3xy + 3y - 5x - 5 is (x + 1)(3y - 5).