Find k so that kx^2 - 12x + 9 is the square of a binomial

k = 4

Step-by-step explanation:

Given polynomial is,

kx² - 12x + 9

We have to find the value of 'k' for which the given polynomial is a square of a binomial.

To find this we will use the formula,

(a - b)² = a² - 2ab + b²

kx² - 12x + 9 = kx² - 2(6x) + 3²

                    = kx² - 2(3)(2x) + 3²

By comparing this with the formula of (a - b)²,

b = 3

a = 2x

(2x)²- 2(2x)(3) + 3² = (2x - 3)²

4x² - 12x + 9 = (2x - 3)²

Therefore, k = 4 will make the polynomial a perfect square of a binomial.

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step-by-step explanation:

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