Answer:
4
Explanation:
You need to find a value that makes this expression a perfect square trinomial. A perfect square trinomial results from squaring a binomial from the form of (a + b)².
When we square (a + b)², we get a² + 2ab + b² (expand and use foil)
Break this into three steps.
Step 1: square the first term (this is where a² came from)
Step 2: Multipy the terms together, then multiply by 2
(a)(b) = ab, then we multiply by 2, giving is 2ab.
Step 3: Square the second term (This is where b² came from)
So we will use these steps to work backwards to get our answer.
Using w² - 4w + k, we need to find a value for k that makes this a perfect square trinomial.
Remember, we are working backwards now, so we do the opposite operation form the steps above
Step 1: We take the square root of the first term (√w² = w)
Step 2: First divide the second term by 2, the result is the product of the 2
terms. (-4w/2 = -2w, so our terms are w and -2)
Step 3: We are given the third term by step 2. Since the first term is w, and the product of the first and second term is -2w, the third term must be -2.
So we square -2 to get the third term in our trinomial. (-2)² = 4