The area of a rectangular painting is given by the trinomial x2 + 4x – 21. What are the possible dimensions of the painting? Use factoring.
A. (x + 7) and (x + 3)
B. (x – 7) and (x + 3)
C. (x – 7) and ( x – 3)
D. (x + 7) and (x – 3)
The trinomial can be factored as (x + 7)(x - 3) by finding factors of -21 that add up to 4. Therefore, the possible dimensions of the painting are x + 7 and x - 3. The answer is D.
To find the possible dimensions of the painting, we need to factor the given trinomial x^2 + 4x - 21.
The first step is to find two numbers whose product is -21 and whose sum is 4. The numbers that satisfy these conditions are -3 and 7.
Therefore, we can factor the trinomial as (x - 3)(x + 7).
The possible dimensions of the painting are (x - 3) and (x + 7).
So, the correct answer is option C: (x - 7) and (x - 3).