The area of a rectangular room is given by the trinomial x squared plus 3 x minus 28. What are the possible dimensions of the rectangle? Use factoring.
A. left parenthesis x minus 7 right parenthesis and left parenthesis x plus 4 right parenthesis
B. left parenthesis x minus 7 right parenthesis and left parenthesis x minus 4 right parenthesis
C. left parenthesis x plus 7 right parenthesis and left parenthesis x plus 4 right parenthesis
D. left parenthesis x plus 7 right parenthesis and left parenthesis x minus 4 right parenthesis
geez - ever think of using actual math expressions?
x^2 + 3x - 28 = (x+7)(x-4)
so what do you think?
To find the possible dimensions of the rectangle, we need to factor the given trinomial: x^2 + 3x - 28.
We can start by looking for two numbers that multiply to -28 (the coefficient of the constant term) and add up to 3 (the coefficient of the x term).
After some trial and error, we find that the numbers 7 and -4 meet these criteria. So we can rewrite the trinomial as:
x^2 + 7x - 4x - 28
Now, we group the terms and factor by grouping:
(x^2 + 7x) + (-4x - 28)
We can factor out an x from the first group and a -4 from the second group:
x(x + 7) - 4(x + 7)
Now, we can see that both terms have a common factor of (x + 7), so we can factor it out:
(x + 7)(x - 4)
Therefore, the factored form of the trinomial x^2 + 3x - 28 is (x + 7)(x - 4).
This means that the possible dimensions of the rectangle are x + 7 and x - 4.
So, the correct answer is option D: (x + 7) and (x - 4).
To find the possible dimensions of the rectangle, we need to factor the trinomial x^2 + 3x - 28.
To factor the trinomial, we need to find two numbers whose product is -28 and whose sum is 3. By testing different pairs of numbers, we can determine that the numbers are 7 and -4.
Therefore, the factored form of the trinomial is (x + 7)(x - 4).
Now, we can see that the possible dimensions of the rectangle are x + 7 and x - 4.
So, the correct answer is D. (x + 7) and (x - 4).