−x2 − 3x3 − x4
Evaluate each polynomial for x = 3 and for x = −3.
Exponent is indicated by "^".
-x^2 - 3x^3 - x^4
You need to use parentheses to indicate the formula more exactly. For example, is it (-x)^2 or -(x^2)? For the value of 3, it would be 9 or -9 respectively. Is the second term -3(x^3) or -(3x)^3?
Get the idea?
To evaluate a polynomial for a given value of x, simply substitute that value into the polynomial expression and perform the necessary calculations.
For x = 3:
Replace every instance of x in the polynomial expression with 3:
(-3)2 - 3(3)3 - (3)4
Now, solve the expression using the order of operations (PEMDAS):
(-9) - 27(3) - 81
Keep in mind that exponents take precedence over multiplication and addition/subtraction:
-9 - 81 - 81
Finally, perform the subtraction:
-9 - 81 - 81 = -171
Therefore, the polynomial evaluates to -171 when x = 3.
For x = -3:
Replace every instance of x in the polynomial expression with -3:
(-(-3))2 - 3(-3)3 - (-3)4
Simplify the expression using the order of operations:
(-3)2 - 3(-27) - 81
Solve the exponent first:
9 - 3(-27) - 81
Next, perform the multiplication:
9 + 81 - 81
Finally, perform the addition and subtraction:
9 + 0 = 9
Therefore, the polynomial evaluates to 9 when x = -3.