To find the value of x that satisfies the equation P(x) = g(x), you need to set the two polynomials equal to each other and solve for x:
P(x) = x^5 + 3x^2 + 2x - 6 g(x) = x^2 + 4
Now, set P(x) equal to g(x) and solve for x:
x^5 + 3x^2 + 2x - 6 = x^2 + 4
First, subtract x^2 and 4 from both sides:
x^5 + 3x^2 + 2x - x^2 - 4 - 6 = 0
Now, combine like terms:
x^5 + 2x^2 + 2x - 10 = 0
This is a polynomial equation of degree 5, and solving it for x can be quite complex. In many cases, it may not have a simple algebraic solution. To find approximate numerical solutions, you can use numerical methods or a graphing calculator.
