Question

k^2 - 13k + 40 is (k - 5)(k - 8)
a. true
b. false

Explanation:

Step1: Expand the right-hand side

To check if \(k^2 - 13k + 40=(k - 5)(k - 8)\), we expand \((k - 5)(k - 8)\) using the distributive property (FOIL method).
First, multiply the First terms: \(k\times k = k^2\).
Then, the Outer terms: \(k\times(-8)=-8k\).
Next, the Inner terms: \(-5\times k=-5k\).
Finally, the Last terms: \(-5\times(-8) = 40\).
Now, combine like terms: \(k^2-8k - 5k+40=k^2-13k + 40\).

Step2: Compare with the left-hand side

The left-hand side of the equation is \(k^2 - 13k + 40\), and after expanding \((k - 5)(k - 8)\) we also get \(k^2 - 13k + 40\). So the factorization is correct.

Answer:

A. True