3x^2+20x+12
if that ^ represnts the area of a rectangle, find two binomials that can represent its dimensions
3x^2+20x+12
x^2+20x+36
(3x+_a_)(3x+_b_)
What times wat =20 is a
and adds up to 36 is b
Then divide a by 3 and b by 3
giving u:
(x+__)(x+__)
then make x = to 0
x+__=0 x+__=0
subtract over the number and you will have your answer
To find two binomials that can represent the dimensions of a rectangle with area 3x^2+20x+12, we need to factor the expression.
The given expression is:
3x^2 + 20x + 12
First, let's look for two numbers that multiply to give 3 * 12 = 36 (the product of the coefficient of the x^2 term and the constant term) and add up to give the coefficient of the x term, which is 20.
The numbers that satisfy these conditions are 6 and 6, because 6 * 6 = 36 and 6 + 6 = 12.
Now we rewrite the expression using these numbers:
3x^2 + 6x + 6x + 12
Next, we group the terms:
(3x^2 + 6x) + (6x + 12)
Now we factor out the greatest common factor from each group:
3x(x + 2) + 6(x + 2)
Notice that we have a common factor of (x + 2) in both terms.
Finally, we can factor out this common binomial:
(x + 2)(3x + 6)
Therefore, the two binomials that represent the dimensions of the rectangle are (x + 2) and (3x + 6).
To find two binomials that can represent the dimensions of a rectangle, we need to factor the quadratic expression. In this case, the quadratic expression is 3x^2+20x+12.
To factor the quadratic expression, we can look for two numbers that multiply together to give the product of the quadratic term (3x^2) and the constant term (12), and at the same time, add up to give the coefficient of the linear term (20x).
In this case, the numbers that satisfy these conditions are 3 and 4.
Let's break down the process step-by-step:
1. First, we look at the coefficient of the quadratic term (3) and the constant term (12).
2. Find two numbers that multiply together to give the product of 3 and 12, which is 36. These numbers are 3 and 12.
3. Next, we look at the coefficient of the linear term (20x). We need to find two numbers that add up to give 20.
4. The two numbers that satisfy these conditions are 3 and 4, as 3 + 4 = 7 and 3 * 4 = 12.
Now that we have identified the numbers, we can rewrite the quadratic expression using these numbers as the coefficients of the middle term:
3x^2 + 20x + 12 can be rewritten as:
3x^2 + 3x + 4x + 12
Next, we group the terms:
(3x^2 + 3x) + (4x + 12)
We can factor out the greatest common factor from each group:
3x(x + 1) + 4(x + 3)
Now we can see that we have two binomials:
(x + 1) and (x + 3)
These two binomials represent the dimensions of the rectangle.
So, the dimensions of the rectangle are (x + 1) and (x + 3).