Question

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Answer 1

These are 2 questions and 2 answers:

1. Question 1: The area of a rectangular carpet is given by the trinomial 5x^2 - 3x - 14. What are the possible dimensions of the carpet? Use factoring.

Answer: 5x^2 -3x  -14

Explanation:

You might probe the different pairs of factors given in the answer choices to check wich product is equal to the oirginal polynomial or you can factor from zero.

I will show  you how to factor that polynomial from zero:

1) given: 5x^2 - 3x - 14

2) multiply and divide by the leading coefficient =>

5 [5x^2 - 3x  -14 ]
----------------------
         5

3) Enter the the factor 5 inside the parenthesis:

5.5x^2 - 5.3x - 5.14
--------------------------
              5

4) rearrange conviniently to show (5x) as a common factir of the first two terms

(5x)^2 - 3(5x) - 70
--------------------------
              5

5) factor the numerator using 5x as common term of the two binomials:

(5x  ) ( 5x   ) <----> open the parenthesis
(5x - ) (5x + ) <-----> include the signs
(5x - 10) (5x + 7)  <---> two numbers that add up - 3 and their product is  - 70

=>

(5x - 10)(5x + 7)
---------------------
         5

6) divide (5x - 10) by 5 => x - 2

7) factored expression

(x - 2) (5x + 7)

8) Conclusion: the answer is the option B. (5x + 7) and (x - 2)


2. Question 2.  The area of a rectangular barnyard is given by the trinomial 6x^2 + 7x – 20. What are the possible dimensions of the barnyard? Use factoring

Answer: option C. (2x + 5)(3x - 4)

Explanation:

The procedure is the same of the question 1.

1) given: 6x^2 + 7x - 20

2) multiply numerator and denominator by 6 and rearrange to show (6x) as common factor ot the first two terms =>

(6x)^2 + 7(6x) - 120
--------------------------
              6
3) factor the numerador using 6x as common factor ot two binomials, and simplify:

(6x + )(6x - )
(6x + )(6x - )
(6x + 15) (6x - 8)

=>

(6x + 15)(6x -8)
---------------------
           6

(6x + 15)(6x - 8)
---------------------- =
        3.2

(6x + 15)      (6x - 8)
------------- .  ------------ =
      3                2

(2x + 5)(3x - 4)

4) answer: option C. (2x + 5)(3x - 4)