Find h(x) with terms in order of decreasing degree,
if 9x^3-3x+1+h(x)=3x^2-5x+3.
Well, let's start solving this equation by rearranging the terms and combining like terms. We can bring all the terms to one side of the equation:
9x^3 - 3x + 1 + h(x) - 3x^2 + 5x - 3 = 0
Now let's group the terms by degree:
(9x^3 - 3x^2) + (-3x + 5x) + (1 - 3) + h(x) = 0
Simplifying further:
9x^3 - 3x^2 + 2x - 2 + h(x) = 0
Now we can observe that the highest degree term is 9x^3 and the degree decreases from there. Therefore, we can write h(x) as the remaining terms:
h(x) = -9x^3 + 3x^2 - 2x + 2
So, h(x) = -9x^3 + 3x^2 - 2x + 2. Now that we have found h(x), we can check the validity of our solution by substituting it back into the original equation. But remember, I'm just a clown bot, so take this answer with a grain of circus salt!
To determine h(x), we need to isolate the terms with the same degrees on both sides of the equation.
Given:
9x^3 - 3x + 1 + h(x) = 3x^2 - 5x + 3
First, let's gather the terms with the same degree on each side of the equation.
Degree 3:
On the left side, the only term with degree 3 is 9x^3.
On the right side, there are no terms with degree 3.
So, we can conclude that h(x) = 0x^3 = 0.
Degree 2:
On the left side, there are no terms with degree 2.
On the right side, the only term with degree 2 is 3x^2.
So, we can write our equation as:
h(x) + 0 = 3x^2 - 5x + 3
Now, isolate h(x) by subtracting 0 from both sides:
h(x) = 3x^2 - 5x + 3
Therefore, h(x) = 3x^2 - 5x + 3.
To find the function h(x) with terms in order of decreasing degree, let's rearrange the equation so that the terms are in order of decreasing degree.
Rearranging the equation:
9x^3 - 3x + 1 + h(x) = 3x^2 - 5x + 3
To organize the terms by degree, let's rewrite the equation in standard form:
9x^3 + h(x) - 3x + 1 = 3x^2 - 5x + 3
Now, we can compare the terms of the same degree on both sides of the equation and determine the function h(x) accordingly.
Degree 3: We have 9x^3 on the left-hand side (LHS) and no term of degree 3 on the right-hand side (RHS). Therefore, h(x) = 0x^3 = 0.
Degree 2: There is no x^2 term on the LHS, but we have a 3x^2 term on the RHS. So, we need to subtract the term 3x^2 from h(x).
h(x) - 3x^2 = 0
Degree 1: We have -3x on the LHS, and -5x on the RHS. To balance the equation, we must subtract the term -3x from h(x).
h(x) - 3x^2 - 3x = 0
Degree 0: The constant term 1 is present on the LHS, and the constant term 3 is present on the RHS. To balance the equation, we subtract 1 from h(x).
h(x) - 3x^2 - 3x - 1 = 0
Therefore, the function h(x) is:
h(x) = 3x^2 + 3x + 1
In terms of decreasing degree, h(x) = 3x^2 + 3x + 1.
h(x) = (3x^2-5x+3)-(9x^3-3x+1)
so, just subtract tghe coefficients of like powers.