Q. Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.h2−6h+____
Identify coefficients and compare: Identify the coefficients of the polynomial h2−6h+? and compare it with the standard quadratic form ax2+bx+c. Here, a=1 and b=−6. We need to find the value of c that makes the polynomial a perfect square.
Calculate half and square: To complete the square, we take half of the coefficient of h, which is −6, and then square it.Half of −6 is −3, so we square −3 to get 9.
Complete the square: The number that completes the square is 9. Therefore, the polynomial becomes a perfect-square quadratic when we add 9 to it.The completed square form is h2−6h+9.