If x² + kx + 6 = (x + 2) (x + 3) for all x, then the value of k is
a. 1
b. -1
c. 5
d. 3

Solution:

Given

x² + kx + 6 = (x + 2) (x + 3)

It can be written as

x² + kx + 6 = x (x + 3) + 2 (x + 3)

Using the multiplicative distributive property

x² + kx + 6 = x² + 3x + 2x + 6

So we get

x² + kx + 6 = x² + 5x + 6

By equating both sides we get

k = 5

Therefore, the value of k is 5.

✦ Try This: If x² + kx + 8 = (x + 5) (x + 7) for all x, then the value of k is

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2

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NCERT Exemplar Class 9 Maths Exercise 2.1 Sample Problem 1

If x² + kx + 6 = (x + 2) (x + 3) for all x, then the value of k is a. 1, b. -1, c. 5, d. 3

Summary:

The standard form of a polynomial refers to writing a polynomial in the descending power of the variable. If x² + kx + 6 = (x + 2) (x + 3) for all x, then the value of k is 5

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