The expression ax^3+2x^2+cx+1 is 5x^3-3 greater than 3x^3+bx^2+d-7x. Find a, b, c, and d.

Well, let's break it down. If we compare the coefficients of the two polynomials, we can determine the values of a, b, c, and d.

For the x^3 terms, we have:
5x^3 - 3 = 3x^3
This means that 5 must be equal to 3, which is clearly not the case. So, no value of a will make this equation true.

Looks like I failed as a mathematician, but hey, at least I'm a funny bot, right?

To find the values of a, b, c, and d, we will compare the corresponding terms of both sides of the equation.

Comparing the x^3 terms:
Coefficient of x^3 on the left side is a, and on the right side is 5.
Therefore, a = 5.

Comparing the x^2 terms:
Coefficient of x^2 on the left side is 2, and on the right side is b.
Therefore, b = 2.

Comparing the x terms:
Coefficient of x on the left side is c, and on the right side is -7.
Therefore, c = -7.

Comparing the constant terms:
Constant term on the left side is 1, and on the right side is d - 3.
Therefore, d - 3 = 1.
Simplifying, we get:
d = 4.

Therefore, the values of a, b, c, and d are:
a = 5, b = 2, c = -7, and d = 4.

To find the values of a, b, c, and d, we need to equate the given expression with the other expression and compare the coefficients of corresponding powers of x.

Let's set up the equation using the given information:

ax^3 + 2x^2 + cx + 1 = (5x^3 - 3) - (3x^3 + bx^2 + d - 7x)

Simplifying the equation by combining like terms, we have:

ax^3 + 2x^2 + cx + 1 = 5x^3 - 3 - 3x^3 - bx^2 - d + 7x

Rearranging the terms in descending order of powers of x, we get:

ax^3 + 2x^2 + cx + 1 = 2x^3 + (7 - b)x^2 + (c + 7)x - (d + 3)

Now we can compare the coefficients on both sides of the equation to find the values of a, b, c, and d.

1. Coefficient of x^3:
On the left side, the coefficient of x^3 is a.
On the right side, the coefficient of x^3 is 2.

Therefore, we have a = 2.

2. Coefficient of x^2:
On the left side, the coefficient of x^2 is 2.
On the right side, the coefficient of x^2 is (7 - b).

Since there is no corresponding x^2 term on the left side, we can equate the coefficients to find b:

2 = 7 - b

Solving for b, we have:
b = 7 - 2
b = 5

3. Coefficient of x:
On the left side, the coefficient of x is c.
On the right side, the coefficient of x is (c + 7).

Since there is no corresponding x term on the left side, we can equate the coefficients to find c:

c = c + 7

This equation indicates that c can have any value since the variable cancels out.

4. Constant term (no x):
On the left side, the constant term is 1.
On the right side, the constant term is -(d + 3).

Therefore, we have:

1 = -(d + 3)

Solving for d, we have:
d + 3 = -1
d = -1 - 3
d = -4

In summary, we have found the values of a, b, c, and d:

a = 2
b = 5
c can be any value
d = -4

ax^3+2x^2+cx+1 -( 5x^3-3)=3x^3+bx^2+d-7x

x^3(a-5-3)+x^2(2-b)+x(c+7)+(1+3)-d)=0

check that

then,if it is right, a=8, b=2, c=-7, d=4