the diagram represents the polynomial 4x² + 23x - 72. what is the factored form of 4x² + 23x - 72? (4x +…

Explanation:

Step 1: Identify coefficients and find factor pair

For (4x^2 + 23x - 72), find two numbers (a, b) such that (a \cdot b = 4 \cdot (-72) = -288) and (a + b = 23). The numbers are (32) and (-9).

Step 2: Split middle term and group

Rewrite polynomial as (4x^2 + 32x - 9x - 72), then group:
((4x^2 + 32x) + (-9x - 72)).

Step 3: Factor out common terms

Factor first group: (4x(x + 8)), second group: (-9(x + 8)).

Step 4: Combine factors

Combine to get ((4x - 9)(x + 8)).

Answer:

(4x − 9)(x + 8)