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

Question

asked Apr 21, 2022 204k views

1 Answer

Vu · Answer 1 · 2022-04-25T16:05:19+0000

Answer:

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.