Eallorise \( x^{2}-10 x+16 \)

It appears you would like to **factorize** the quadratic expression: \[ x^{2} - 10x + 16 \] To factorize this quadratic, we look for two numbers that satisfy the following conditions: 1. **Sum**: The numbers should add up to the coefficient of the \( x \) term, which is **-10**. 2. **Product**: The numbers should multiply to the constant term, which is **16**. Let's find such numbers: - Consider the pairs of factors for 16: - \( 1 \) and \( 16 \) → \( 1 + 16 = 17 \) (Not -10) - \( 2 \) and \( 8 \) → \( 2 + 8 = 10 \) (We need -10) - \( 4 \) and \( 4 \) → \( 4 + 4 = 8 \) (Not -10) Since we need the sum to be **-10**, we can take both factors as negative: - \( -2 \) and \( -8 \) → \( -2 + (-8) = -10 \) and \( (-2) \times (-8) = 16 \) Now, we can express the quadratic as: \[ x^{2} - 10x + 16 = (x - 2)(x - 8) \] **Verification:** \[ (x - 2)(x - 8) = x \cdot x - 8x - 2x + 16 = x^{2} - 10x + 16 \] Thus, the factorized form of \( x^{2} - 10x + 16 \) is: \[ (x - 2)(x - 8) \]