the area of a rectangle painting is given by the trinomial a^2-14a+45. the painting length is (a+2). what is the painting width?
long division
a-16 and remainder = 77/(a^2-14a+45)
do you have a typo by any chance?
To find the width of the rectangle painting, we need to first factor the given trinomial. Let's factor the trinomial a^2 -14a + 45:
a^2 -14a + 45 = (a - 9)(a - 5)
Now that we have factored the trinomial, we can see that it can be expressed as the product of two binomials: (a - 9) and (a - 5).
Since the painting's length is given as (a + 2), we equate it to one of the binomials (a - 9) since they represent the length and width of the rectangle:
a + 2 = a - 9
Next, we solve for 'a':
2 = -9
In this equation, we can see that there is no solution for 'a'. This means that there is no valid width for the given length of (a + 2). Consequently, there may be an error in the problem statement or some other information is missing.