Determine the binomials that represent the dimensions ( length and width ) of a rectangular garden if the area of the gardfen is A=x^2+ 5x + . Then, determine the dimensions of the garden if X represents 1 M
I got y = (x+3) (x+2)
your solution fits if you mean x^2+5x+6 which factors out to (x+3)(x+2)
the binomials are just x+3 and x+2
So, the garden is 4 by 3
To determine the binomials that represent the dimensions of the rectangular garden, we need to factorize the given quadratic expression for the area.
The given quadratic expression for the area of the garden is A = x^2 + 5x + c, where c represents a constant term that is missing in the given information.
To factorize the quadratic expression, we need to find two binomials in the form (x + m) and (x + n), where m and n are constants, such that when we multiply them, we get the quadratic expression.
In this case, we need to find two binomials in the form (x + m) and (x + n) such that:
(x + m) * (x + n) = x^2 + 5x + c
To find the values of m and n, we can use the following techniques:
1. Splitting the middle term: We can split the middle term (5x) into two parts such that their sum is equal to the coefficient of the middle term. In this case, the coefficient of the middle term is 5. So, we need to find two numbers whose sum is 5 and whose product is equal to the product of the coefficient of x^2 term (1) and the constant term (c).
2. Factoring by grouping: We can group the first two terms and the last two terms separately and look for a common factor to factorize the expression.
However, since the value of the constant term (c) is not provided in the question, we cannot determine the exact binomials that represent the dimensions of the garden.
To determine the dimensions of the garden when x represents 1 meter, we can substitute x = 1 into the given quadratic expression for the area.
So, when x = 1,
A = (1)^2 + 5(1) + c
A = 1 + 5 + c
A = 6 + c
Therefore, the area of the garden when x represents 1 meter is A = 6 + c square meters.