Given that the area of the rectangle is 2x^2 + 9x - 5 , determine the length of the rectangle.
not enough information.
Sorry the width is x+5, I think I combine the like terms, is that right?
no
Area = length x width
so
2x^2 + 9x - 5 = (x+5)(.......)
you can do either a division, or just use common sense
where does the 2x^2 come from?
Wouldn't it be the multiplication of the first terms in the binomials?
where does the - 5 come from?
wouldn't it be the multiplication of the last numbers of the 2 binomials?
x^2-1
would it be this?
no.
what multiplied by (x+5) gives (2x^2+9x+5)?
Think. What multiplied by x gives 2x^2?
then what multliplied by 5 gives 5?
(??? +???)
2x-1
To determine the length of the rectangle, we need to factor the given quadratic expression, which represents the area of the rectangle.
The quadratic expression is: 2x^2 + 9x - 5
Step 1: Multiply the coefficient of the x^2 term (2) by the constant term (-5).
2 * -5 = -10
Step 2: Find two numbers that multiply to give -10 and add up to the coefficient of the x term (9). In this case, the numbers are 10 and -1.
10 * -1 = -10
10 + (-1) = 9
Step 3: Rewrite the quadratic expression by splitting the x term using the numbers from step 2.
2x^2 + 10x -x - 5
Step 4: Group the terms:
(2x^2 + 10x) + (-x - 5)
Step 5: Factor out the greatest common factor (GCF) from each group:
2x(x + 5) - (x + 5)
Step 6: Notice that both groups now share a common factor of (x + 5).
(2x - 1) (x + 5)
The factored form of the quadratic expression is: (2x - 1) (x + 5)
Now, we can determine the length of the rectangle. Since the length corresponds to one of the factors, we look for the factor that does not have an x term. In this case, it is (x + 5).
Therefore, the length of the rectangle is x + 5.