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Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728

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Chapter
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BuyFindarrow_forward

Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728
Textbook Problem

For problems 31-56, factor completely each of the trinomials and indicate any that are not factorable using integers. (Objective 2)

15 x 2 + 23 x + 6 .

To determine

To factor:

The given expression 15x2+23x+6.

Explanation

Procedure:

To factor the trinomials in the form of ax2+bx+c, we follow the steps given below:

Step-1: Multiply the coefficients of x2 and the constant term. That is a·c.

Step-2: Find the integers whose sum is equal to b=a+c and whose product is a·c.

Step-3: List out the pairs of factors for a·c preferably using a table.

Step-4: Rewrite the original problem by splitting the appropriate terms.

Step-5: Now, use the factoring by grouping method to factor the rewritten problem and simplify to get the solution.

Calculation:

Given expression:15x2+23x+6.

We need to complete the following with two integers whose sum is 23 and whose product is 90.

15x2+23x+6=15x+__x+__

The following table shows the possible pairs of factors of 90:

Factors Product of the factors Sum of the factors
190 90 91
245 90 47
330 90 33
518 90 23
615 90 21
910 90 19

From the above table, we find that the numbers that we need are 5 and 18 and we can complete the factoring

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