The area of a rectangle is 8x2+22x+15
8
x
2
+
22
x
+
15
. What are the possible dimensions of the rectangle? Use factoring.(1 point)
To find the possible dimensions of the rectangle, we need to factor the expression 8x^2 + 22x + 15.
We start by looking for two numbers that multiply to 8 * 15 = 120 and add up to 22. The numbers that satisfy these conditions are 10 and 12.
Therefore, we rewrite the expression: 8x^2 + 10x + 12x + 15
Now, we can factor by grouping:
(8x^2 + 10x) + (12x + 15)
2x(4x + 5) + 3(4x + 5)
(2x + 3)(4x + 5)
So, the possible dimensions of the rectangle are 2x + 3 and 4x + 5.
I don't understand
I apologize for the confusion. Let me explain it in simpler terms:
Given the area of the rectangle in the form of 8x^2 + 22x + 15, we want to find the possible dimensions of the rectangle.
To do this, we need to factor the expression. Here's how we can do it:
1. First, we identify two numbers that multiply to 8 * 15 = 120 and add up to 22. The numbers are 10 and 12.
2. Next, we rewrite the expression as: 8x^2 + 10x + 12x + 15
3. Now, we group the terms and factor by grouping:
(8x^2 + 10x) + (12x + 15)
2x(4x + 5) + 3(4x + 5)
(2x + 3)(4x + 5)
4. The factored expression is (2x + 3)(4x + 5).
Therefore, the possible dimensions of the rectangle are the factors of the factored expression:
Length = 2x + 3
Width = 4x + 5
These are the dimensions of the rectangle based on the factored expression of the area.
can you give me the answer without the example
Of course! The possible dimensions of the rectangle based on the factored expression 8x^2 + 22x + 15 are:
Length = 2x + 3
Width = 4x + 5
These are the dimensions of the rectangle.