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Intermediate Algebra

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

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BuyFindarrow_forward

Intermediate Algebra

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

Thoughts Into Words

Consider the following approach to factoring 12 x 2 + 54 x + 60 :

12 x 2 + 54 x + 60 = 3 x + 6 4 x + 10

= 3 x + 2 2 2 x + 5

= 6 x + 2 2 x + 5

Is this a correct factoring process? Do you have a suggestion for a person using this approach?

To determine

To explain:

The approach for factoring of a trinomial 12x2+54x+60 is a correct factoring process and provide the suggestion for a person using the given approach.

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 trinomial: 12x2+54x+60.

Given approach: 12x2+54x+60=3x+64x+10

=3x+222x+5

=6x+22x+5

The final solution for factoring the given trinomial 12x2+54x+60 is correct. But this approach is not correct.

To factor the given trinomial 12x2+54x+60, the following procedure must be used.

Rewriting the given trinomial 12x2+54x+60=62x2+9x+10

We need to complete the following with two integers whose sum is 9 and whose product is 2×10=20.

12x2+54x+60=62x+__x+__

The following table shows the possible pairs of factors of 20:

Factors Product of the factors Sum of the factors
120 20 21
210 20 22
45 20 9

From the above table, we find that the numbers that we need are 4 and 5 and we can complete the factoring

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