1. **Statement of the problem:** Factor the expression $$A = (x+1)(-x+5) + (x+1)(-6+4x)$$ into a product of two factors. 2. **Formula and rules:** Use the distributive property to factor common terms: $$a(b+c) = ab + ac$$. 3. **Intermediate work:** $$A = (x+1)(-x+5) + (x+1)(-6+4x)$$ Factor out the common factor $$(x+1)$$: $$A = (x+1)\big((-x+5) + (-6+4x)\big)$$ Simplify inside the parentheses: $$(-x+5) + (-6+4x) = -x + 5 - 6 + 4x = (-x + 4x) + (5 - 6) = 3x - 1$$ So, $$A = (x+1)(3x - 1)$$ **Final answer:** $$A = (x+1)(3x - 1)$$