Question

X2-x-42=(x+k)(x+6) find the value of k

Answer 1

this is the answer

hope it will help

Answer 2

Given,

x²-x-42 = (x+k)(x+6)

To find,

The value of k.

Solution,

The value of k will be -7.

We can easily solve this problem by following the given steps.

According to the question,

x²-x-42 = (x+k)(x+6)

Let's factorise the expression on the left-hand side by splitting the middle term such that their subtraction will be (-x) and their multiplication will be (-42×x²).

These two terms are (-7x) and 6x.

x²-7x+6x-42

Taking x common from the first two terms and 6 common from the last two terms,

x(x-7)+6(x-7)

Taking (x-7) common,

(x-7) (x+6)

So, we have

(x-7) (x+6) = (x+k) (x+6)

Dividing (x+6) by (x+6),

(x-7) = (x+k)

(x+k) = (x-7)

k = x-x-7

k = -7

Hence, the value of k is -7.