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Intermediate Algebra

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

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Chapter
Section
BuyFindarrow_forward

Intermediate Algebra

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

Problems 63-112 should help you pull together all of the factoring techniques of this chapter. Factor completely each polynomial, and indicate any that are not factorable using integers. (Objective 4)

18 n 3 + 39 n 2 - 15 n .

To determine

To factor:

The given expression 18n3+39n2-15n.

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: 18n3+39n2-15n.

Factoring the common term 3n out, we get

=3n6n2+13n-5

We need to complete the following with two integers whose sum is 13 and whose product is -30.

18n3+39n2-15n=3n6n2+13n-5=3n6n+__n+__

The following table shows the possible pairs of factors of -30:

Factors Sum of the factors
1-30 -29
2-15 -13
3-10 -10
5-6 -1

From the above table, we find that the numbers that we need are 3 and -10 and we can complete the factoring

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