Question

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✔Question 17
The expressions 2(2²-42-21)-(z-7)(z+77) and (z-7)(z+k) are equivalent.
What must be the value of k?
B
C
-148
-71
83
160

Answer 1

To find the value of k, we need to set the two given expressions equal to each other and solve for k.

First, let's expand the first expression: 2(2²-42-21)-(z-7)(z+77) = 4 - 8 - 42 - 21 - (z-7)(z+77) = -47 - (z-7)(z+77)

Now, let's set this equal to the second expression: -47 - (z-7)(z+77) = (z-7)(z+k)

Expanding the second expression, we get: -47 - (z-7)(z+k) = z^2 - 7z + zk - 7k

Matching the coefficients of like terms, we get:

-47 = z^2 - 7z + zk - 7k
-47 = z^2 + zk - 7z - 7k
0 = z^2 + zk - 7z - 7k + 47
0 = (z-7)(z+k) + 47

Since the expression in parentheses is equal to zero, we have:

0 = 47

This equation has no solutions, so the given expressions are not equivalent. This means that we cannot find a value of k that makes the two expressions equal.

Therefore, the answer is none of the given options.