The expression X^2(x+3)-9(x+3) is equivalent to (x+3)^n(x-3) when n equals?
I got an answer of 2
I did X^2(x+3)-9(x+3) (x+3)^n(x-3)
4(5)-9(5)=-25 -25=(5)^n(-1)
n=2
Is this correct? Thank you for checking my work
looks good
Thank you
To determine the value of n, we need to equate the two expressions and solve for n.
Starting with X^2(x+3)-9(x+3):
= x^2(x+3) - 9(x+3)
= (x^2 - 9)(x+3)
= (x+3)(x+3)(x-3)
= (x+3)^2(x-3)
So, we have (x+3)^n(x-3) = (x+3)^2(x-3)
By comparing the expressions, we can conclude that n = 2.
Therefore, your answer of n = 2 is correct.
Let's go through the steps to solve this problem.
Step 1: Simplify the expression X^2 (x + 3) - 9 (x + 3)
To simplify this expression, you distribute the X^2 and -9 to both terms inside the parentheses:
X^2 (x) + X^2 (3) - 9 (x) - 9 (3)
Simplifying further will give you:
X^3 + 3X^2 - 9x - 27
Step 2: Simplify the expression (x + 3)^n (x - 3)
Since (x + 3)^n (x - 3) cannot be further simplified without knowing the value of n, we have to find the value of n in order to equate the two expressions.
Step 3: Equate the two expressions
Set the simplified expressions from the previous steps equal to each other:
X^3 + 3X^2 - 9x - 27 = (x + 3)^n (x - 3)
Step 4: Find the value of n
To find the value of n, we need to compare the powers of x on both sides of the equation.
On the left side, the highest power of x is x^3. On the right side, the highest power of x is (x + 3) multiplied by (x - 3), which simplifies to x^2 - 9.
Since the highest power of x on the left side is x^3, and on the right side is x^2, we can conclude that n = 3.
So, n is equal to 3, not 2 as you mentioned.