Question

Help pls and explain!!!

If x^2 + kx + 6 = (x+n)(x + 3) for all values of x, where k and n are constants, what is the value of k?
A) 5
B) 3
C) 2
D) 1

Answer 1

A) 5

Explanation:

We are given that:

`x^2+kx+6=(x+n)(x+3)`

Where k and n are constants.

And we want to find the value of k.

We can expand the right-hand side:

`\displaystyle =x(x+n)+3(x+n)\\ \\ = x^2+nx+3x+3n \\ \\ = x^2 + (n+3)x+3n`

Hence:

`x^2+kx+6=x^2+(n+3)x+3n`

The coefficients of each term must be equivalent. In other words:

`k=n+3\text{ and } 6=3n`

Solve for n:

`n=2`

Now, we can solve for k:

`k=(2)+3=5`

Our answer is A.