Evaluate the expression when c = -6. c² + 5c - 1
Understand the Problem
The question is asking us to evaluate the expression c² + 5c - 1 by substituting c with -6. This involves plugging the value of c into the expression and calculating the result.
Answer
The result of the expression $c^2 + 5c - 1$ when $c = -6$ is $5$.
Answer for screen readers
The final answer is $5$.
Steps to Solve
- Substitute the value of c
To evaluate the expression $c^2 + 5c - 1$ when $c = -6$, we start by substituting $-6$ in place of $c$.
$$ (-6)^2 + 5(-6) - 1 $$
- Calculate $c^2$
Next, we calculate $(-6)^2$.
$$ (-6)^2 = 36 $$
- Calculate $5c$
Now we calculate $5(-6)$.
$$ 5(-6) = -30 $$
- Combine the terms
Now we combine all the terms together:
$$ 36 - 30 - 1 $$
- Perform the arithmetic operations
First, we subtract $30$ from $36$, then subtract $1$:
$$ 36 - 30 = 6 $$
$$ 6 - 1 = 5 $$
The final answer is $5$.
More Information
This expression illustrates how to substitute a negative value into a polynomial. Evaluating polynomial expressions is a fundamental skill in algebra.
Tips
- Confusing the order of operations can lead to errors. Always perform exponents first, followed by multiplication, and then addition/subtraction.
- Forgetting to square the negative number (e.g., thinking $(-6)^2 = -36$ instead of $36$).
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