Factorize the polynomial \( 4x^2 - 16x + 16 \)
Answer
Step 3: Expanding \( 4 (x - 2)^2 \), we get \( 4x^2 - 16x + 16 \) which is same as our original polynomial. Therefore, the factorized form of the polynomial \( 4x^2 - 16x + 16 \) is \( 4 (x - 2)^2 \).
Step 1 ：Step 1: Prepare the quadratic expression in the form of \( ax^2 - bx + c \). Here, it is already in the required form, where \( a = 4, b = 16, c = 16 \).
Step 2 ：Step 2: Check if this quadratic expression can be written as \( a (x - h)^2 \). Here, \( h = \frac{b}{2a} = \frac{16}{2*4} = 2 \). Substituting \( h = 2 \) in \( a (x - h)^2 \), we get \( 4 (x - 2)^2 \).
Step 3 ：Step 3: Expanding \( 4 (x - 2)^2 \), we get \( 4x^2 - 16x + 16 \) which is same as our original polynomial. Therefore, the factorized form of the polynomial \( 4x^2 - 16x + 16 \) is \( 4 (x - 2)^2 \).
