The area of a rectangular table is given by the trinomial x2 + 7x – 30. What are the possible dimensions of the rectangle? Use factoring.
(x+10) and(x-3)
Rose is correct
Oh, I'm glad you used the word "factoring" because that's what I'm an expert at. I love factoring almost as much as I love juggling. Alright, let's figure this out!
If we have the trinomial x^2 + 7x - 30, we need to find two numbers that multiply to -30 and add up to 7. This is where it gets exciting!
So, let's try a little "clown magic" with some numbers, shall we? Let's think... how about 10 and -3? They multiply to -30 and add up to 7. Ta-daaa!
Now, let's use these numbers to rewrite the trinomial as two binomials. We have (x + 10) and (x - 3). So, the possible dimensions of the rectangular table are (x + 10) and (x - 3).
Remember, factoring can be a lot of fun once you get the hang of it. And just like a clown with a never-ending supply of tricks, factoring can always come to the rescue!
To find the possible dimensions of the rectangle, we need to factor the given trinomial, x^2 + 7x - 30.
The factors of the trinomial will give us the dimensions of the rectangle.
Step 1: Factor the trinomial.
We need to find two numbers whose sum is 7 and whose product is -30.
x^2 + 7x - 30 = (x + 10)(x - 3)
So, the factored form of the trinomial is (x + 10)(x - 3).
Step 2: Determine the dimensions.
The dimensions of the rectangle can be derived from the factors of the trinomial. In this case, the dimensions are (x + 10) and (x - 3).
So, the possible dimensions of the rectangle are:
Length: x + 10
Width: x - 3
Note: The dimensions may vary depending on the value of x.
Hint for the factors:
Can you think of 2 numbers, one positive and the other negative, which when multiplied give you -30 and when added give you +7 ?