f(x)=x8+7x2+613(x−1)2(x+6)6
The given expression is a polynomial function of x. To evaluate it, you will need to substitute a value for x and simplify the expression.
Let's break down the expression f(x) step by step:
f(x) = x^8 + 7x^2 + 613(x - 1)^2(x + 6)^6
1. Start by simplifying the expression inside the parentheses:
(x - 1)^2 = (x - 1)(x - 1) = x^2 - 2x + 1
2. Next, simplify the expression (x + 6)^6 by expanding it using the binomial theorem:
(x + 6)^6 = (6 choose 0)6^0 * x^6 + (6 choose 1)6^1 * x^5 * 6 + (6 choose 2)6^2 * x^4 * 36 + ...
3. Now, substitute the simplified expressions back into the original expression for f(x):
f(x) = x^8 + 7x^2 + 613(x^2 - 2x + 1)(x + 6)^6
4. Expand the expression by distributing the coefficients:
f(x) = x^8 + 7x^2 + 613(x^2 - 2x + 1)(6^0 * x^6 + 6^1 * x^5 * 6 + 6^2 * x^4 * 36 + ...)
5. Simplify and collect like terms:
f(x) = x^8 + 7x^2 + 613(x^2 - 2x + 1)(x^6 + 6x^5 * 6 + 36x^4 * 6^2 + ...)
6. Continue simplifying by distributing the coefficients and combining like terms.
To evaluate f(x) at a specific value of x, simply substitute that value into the expression and calculate the result.