Answer:
k = 4
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.