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Chapter 8: Q20. (page 514)

Use the Distributive Property to factor each polynomial.

12x+24y

Short Answer

Expert verified

The factorization of the given polynomial is 12x+2y.

Step by step solution

01

Step 1. Find the greatest common factor of 12x and 24y.

Find the factorization of 12xand 24y.

localid="1647527640236" 12x=2鈰�2鈰�3鈰�x24y=2鈰�2鈰�2鈰�3鈰�y

From the factorization of 12xand 24y, it can be noticed that the greatest common factor of 12xand 24yis 2鈰�2鈰�3or 12.

Therefore, the greatest common factor of 12xand 24yis 12.

02

Step 2. Write each term as the product of the greatest common factor and the remaining factors.

Therefore, it is obtained that:

12x+24y=12x+122y

03

Step 3. Use the distributive property to factor out the greatest common factor.

The distributive property states that:

ab+ac=ab+c

Now, use the distributive property to factor out the greatest common factor.

Therefore, it is obtained that:

12x+24y=12x+122y=12x+2y

Therefore, the factorization of the given polynomial is 12x+2y.

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