To find the value of \( k \) when -5 is a zero of the polynomial \( 3x^2 + 8x - k \), follow these detailed steps:
1. Understanding the Problem:
- We are given the polynomial \( 3x^2 + 8x - k \).
- We know that -5 is a zero of this polynomial. This means that if we substitute \( x = -5 \) into the polynomial, the value should be zero.
2. Substitute -5 into the Polynomial:
- Start by substituting \( x = -5 \) into the given polynomial:
[tex]\[
3(-5)^2 + 8(-5) - k = 0
\][/tex]
3. Evaluate the Expression:
- Now, calculate each term in the polynomial:
- First, calculate \((-5)^2\):
[tex]\[
(-5)^2 = 25
\][/tex]
- Next, multiply by the coefficient of \( x^2 \):
[tex]\[
3 \times 25 = 75
\][/tex]
- Then, calculate \( 8 \times (-5) \):
[tex]\[
8 \times (-5) = -40
\][/tex]
- Substitute these results back into our equation:
[tex]\[
75 - 40 - k = 0
\][/tex]
4. Simplify the Equation:
- Combine the constant terms:
[tex]\[
75 - 40 = 35
\][/tex]
- So the equation simplifies to:
[tex]\[
35 - k = 0
\][/tex]
5. Solve for \( k \):
- Isolate \( k \) by adding \( k \) to both sides of the equation:
[tex]\[
35 - k + k = 0 + k
\][/tex]
- This results in:
[tex]\[
35 = k
\][/tex]
6. Conclusion:
- The value of \( k \) is 35.
Therefore, if -5 is a zero of the polynomial [tex]\( 3x^2 + 8x - k \)[/tex], then the value of [tex]\( k \)[/tex] is [tex]\( 35 \)[/tex].
