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Chapter 6: Q. 344 (page 634)

In the following exercises, factor the greatest common factor from each polynomial.

15m4+6m2n

Short Answer

Expert verified

The factored form of the polynomial is3m25m2+2n.

Step by step solution

01

Step 1. Given information.

The polynomial is,

15m4+6m2n.

02

Step 2. Finding the greatest common factor. 

Now, the greatest common factor for the given polynomial will be

15m4+6m2n鈬�15m4=3脳5脳m脳m脳m脳m鈬�6m2n=2脳3脳m脳m脳n

Then the greatest common factor is

3脳m脳m=3m2.

03

Step 3. Factoring the polynomial. 

Now using distributive property factor the polynomial.

15m4+6m2n=3m2脳5m2+3m2脳2n=3m25m2+2n

Hence, the simplified polynomial is 3m25m2+2n.

04

Step 4. Checking the result.

Multiplying the factors we get,

3m25m2+2n=15m4+6m2n.

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