To evaluate polynomials, you start by combining any like terms.
Here is an example:
Evaluate the following polynomial for f(2)
F(x) = 3x4 + 2x2– x4 + 3x3
+ 5
3x4 and –x4 are like terms. They combine
to form 2x4.
F(x) = 2x4 + 2x2 + 3x3 +5
Now, substitute the given value for x
F(2) = 2(2)4 + 2(2)2 + 3(2)3 +5
Order of operations says to do exponents first when evaluating:
2 · 16 + 2 · 4 + 3 · 8 + 5
Next, complete the multiplication:
32 + 8 + 24 + 5 = 69
Example 2
You can follow the same procedure when there are two variables,
such as the following:
Evaluate for x = 4 and y = 3
3xy + 7x2y – 4xy + 9x2y + 5xy2
Start by simplifying by combining like terms.
-1xy + 16x2y + 5xy2
Now, substitute values for the variables
-1(4)(3) +16(4)2(3) + 9(4)2(3) + 5(4)(3)2
Use the order of operations to solve:
-1(4)(3) +16(16)(3) + 9(16)(3) +5(4)(9)
-12 + 768 + 432 + 180 = 1368
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Example 3
The process remains the same, no matter how complicated the problem
becomes. Here is a final example:
Evaluate for x = -3 and y = 9
There are no like terms, so substitute in the variables
Solve, using order of operations.
-3 – (-27) + 4(9) - 
-3 + 27 + 36 + 3 = 63
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