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Chapter 8: Q15. (page 492)

Factor each polynomial.

5a2鈭�25a鈭�a+5

Short Answer

Expert verified

The factors of given polynomial are 5a鈭�1a鈭�5.

Step by step solution

01

Step 1. Combine.

Combine like terms in the given polynomial.

5a2鈭�26a+5

02

Step 2. Find the GCF.

Find the GCF of5a2,26aand 5.

5a2=1鈰�5鈰�a鈰�a26a=1鈰�2鈰�13鈰�a5=1鈰�5

Therefore, GCF is 1.

03

Step 3. Apply factoring pattern of ax2+bx+c.

There are two numbers having product of 25 and sum of -26. The numbers are -1and -25.

5a2+mx+nx+5=5a2鈭�25a鈭�1a+5

04

Step 4. Group terms with common factors and factor out GCF.

Group terms with common factors and factor out GCF from each grouping.

5a2鈭�25a+鈭�1a+5=5aa鈭�5鈭�1a鈭�5=5a鈭�1a鈭�5

Therefore, the factors of5a2鈭�25a鈭�a+5 are 5a鈭�1a鈭�5.

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