Question

Given the quadratic expression y2−9y+20 as (y−5)(y−___). Can you determine the missing factor in order to achieve a complete factorization?

A. y−1
B. y+1
C. y−4
D. y+4

Answer 1

The missing factor to complete the factorization of the quadratic expression y²−9y+20 as (y−5)(y−___) is determined to be y−4, which is option C.

Step-by-step explanation:

The quadratic expression in question is y2−9y+20. We are given the factorized form as (y−5)(y−___), and we are asked to find the missing factor to achieve complete factorization.

To determine the missing factor, we can use the fact that when two binomials are multiplied, the product of the last terms of the binomials must equal the constant term in the quadratic expression.

In this case, the constant term is +20. Since one of the factors is (y−5), the missing number must multiply with -5 to give us +20. Let's denote this missing number as 'b' and set up the equation:

-5 × b = +20

Solving for 'b' gives us b = -4. Therefore, the missing factor is y−4, which is option C.So, the complete factorization of the quadratic expression y2−9y+20 is (y−5)(y−4).