Question

What is the missing factor? (n−5)(?)=2n²−13n+15

a) 2n−3
b) n−3
c) 2n+3
d) n+3

Answer 1

The missing factor in the expression (n-5)(?)=2n²-13n+15 is (2n-3), corresponding to option (a).

Step-by-step explanation:

To determine what the missing factor is in the expression (n−5)(?)=2n²−13n+15, we need to perform polynomial multiplication on the given factors and compare coefficients with the expanded form on the right side. Now, we assume that the missing factor is in the form of (xn + y), where x and y are coefficients we need to find.

Let's multiply (n−5) by a general binomial (xn + y):

• n times xn gives us xn².
• n times y gives us yn.
• (−5) times xn gives us −5xn.
• (−5) times y gives us −5y.

Combining these terms, we get xn² + (y − 5x)n − 5y. Comparing this with 2n²−13n+15, we can equate coefficients:

• For the n² term: x must be 2.
• For the n term: y − 5x = −13; plugging in x = 2 gives y − 10 = −13, hence y = −3.
• For the constant term: −5y = 15; as y = −3, this is confirmed.

Therefore, the missing factor is (2n − 3), which corresponds to option (a).