<span>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: </span><span><span>option C. (2x + 5)(3x - 4)</span>
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:
Step-by-step explanation: To make an improper fraction out of a mixed one we have to multiply the denominator by the whole number (in this case is 4) and then add the numerator. So 7 x 4 = 28 + 2 = 30, so 30/7 would be the correct answer choice.
