91Ó°ÊÓ

Given expression: \(16x^2 - 76x + 21\) Let's list down the pairs of factors of the quadratic term's coefficient: - 16: (1, 16), (2, 8), (4, 4) And for the constant term: - 21: (1, 21), (3, 7)

Now we need to try different combinations of factor pairs to determine the correct binomials. We'll start by forming the two terms for these binomials using these factor pairs. - If we take (2, 8) as the factors of 16, we could have 2x and 8x - If we take (3, 7) as the factors of 21, we could have 3 and 7 Now, we need to see if there is any possible combination of factors that results in the middle term -76x. Let's explore all the possible combinations: 1. (2x + 3)(8x + 7) => 14x + 24x = 38x ≠ -76x 2. (2x + 7)(8x + 3) => 6x + 56x = 62x ≠ -76x 3. (2x - 3)(8x - 7) => (-6x -24x) = -30x ≠ -76x 4. (2x - 7)(8x - 3) => (-14x - 16x) = -30x ≠ -76x It appears that none of the possible combinations of factors result in the middle term -76x.

The quadratic expression \(16x^2 - 76x + 21\) cannot be factored into rational factors, as we have tried all possible combinations and none of them result in the given expression.