Chapter A.2, Problem 44E

Solution

To factor out the common factor of the expression $2x\left(x+3\right)-5\left(x+3\right)$ .

  $\left(x+3\right)\left(2x-5\right)$

Given:

The expression, $2x\left(x+3\right)-5\left(x+3\right)$

Concept Used:

• Like terms are the terms that contain the same variable with similar exponents on it. Constants are like terms as well.
• In any expression, terms are separated by plus or minus signs.
• Coefficients are the constants in front of the variable terms.

Calculation:

In order to find the common factor out first find the common factor in this equation $2x\left(x+3\right)-5\left(x+3\right)$

The common factor in this equation is $\left(x+3\right)$ ,

Therefore putting $\left(x+3\right)$ in front of a set of bracket as shown below:

  $\left(x+3\right)\left(2x-5\right)$

It is $\left(x+3\right)$ times $2x$ and $\left(x+3\right)\times 5$ to get the answer in the bracket.

So, the common factor is $\left(x+3\right)$ .