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?

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

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Ngọc Hoa 5 years 2021-07-24T00:17:19+00:00 1 Answers 10 views 0

Answers ( )

  1. Delwyn
    0
    2021-07-24T00:18:39+00:00
    Reply

    Answer:

    A) 5

    Step-by-step 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.

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