To find a polynomial of degree 3 that satisfies the given conditions, we can start by assuming that the polynomial is of the form:
f(x) = a(x)(x-1)(x+2)
Here, "a(x)" represents a factor that we need to determine. We can simplify this expression as follows:
f(x) = a(x)(x^2 - x + 2x - 2)
f(x) = a(x)(x^2 + x - 2)
Now, to find the value of "a(x)", we can substitute x = 2 into the given condition f(2) = 4:
4 = a(2)(2^2 + 2 - 2)
4 = a(2)(4 + 2 - 2)
4 = a(2)(4)
Dividing both sides by 4:
1 = a(2)
So, "a(2)" is equal to 1. Therefore, we can rewrite the polynomial as:
f(x) = 1(x)(x^2 + x - 2)
f(x) = x(x^2 + x - 2)
And this is the polynomial of degree 3 that satisfies the given conditions.
