Chapter 8: Q15. (page 492)

Factor each polynomial.
$5 a^{2} - 25 a - a + 5$

Short Answer

Expert verified

The factors of given polynomial are $(5 a - 1) (a - 5)$ .

Step by step solution

Step 1. Combine.

Combine like terms in the given polynomial.

$5 a^{2} - 26 a + 5$

Step 2. Find the GCF.

Find the GCF of $5 a^{2}, 26 a$ and 5.

$5 a^{2} = 1 \cdot 5 \cdot a \cdot a 26 a = 1 \cdot 2 \cdot 13 \cdot a 5 = 1 \cdot 5$

Therefore, GCF is 1.

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

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

$5 a^{2} + m x + n x + 5 = 5 a^{2} - 25 a - 1 a + 5$

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

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

$(5 a^{2} - 25 a) + (- 1 a + 5) = 5 a (a - 5) - 1 (a - 5) = (5 a - 1) (a - 5)$

Therefore, the factors of $5 a^{2} - 25 a - a + 5$ are $(5 a - 1) (a - 5)$ .

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Factor each polynomial.
$5 a^{2} - 25 a - a + 5$

Short Answer

Step by step solution

Step 1. Combine.

Step 2. Find the GCF.

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

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

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Factor each polynomial.5a2−25a−a+5

Short Answer

Step by step solution

Step 1. Combine.

Step 2. Find the GCF.

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

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Decision Maths

Pure Maths

Statistics

Logic and Functions

Geometry

Study anywhere. Anytime. Across all devices.

Factor each polynomial.
$5 a^{2} - 25 a - a + 5$