factoring perfect square trinomial8.x²-10x+25
Answer (1)
Answer:8x² - 10x + 25 is not a perfect square trinomial and cannot be factored over the real numbers.Step-by-step explanation:Step 1: Recall the form of a perfect square trinomiala² + 2ab + b² = (a + b)²a² - 2ab + b² = (a - b)²Step 2: Compare the trinomial with the formulaFirst term: 8x² → not a perfect square (since 8 is not a square number).Last term: 25 = 5² → this is a perfect square.Middle term: -10x → does not fit the relationship needed for a perfect square trinomial.Therefore, 8x² - 10x + 25 is NOT a perfect square trinomial.Step 3: Check if the trinomial can be factoredThe quadratic is: 8x² - 10x + 25Use the discriminant formula: D = b² - 4acHere, a = 8, b = -10, c = 25D = (-10)² - 4(8)(25)D = 100 - 800D = -700Since the discriminant is negative, the quadratic has no real factors.
