Factor down the following trinomials.1. 3x²-7x+42. 4x²+8x+43.5x²-2x-34.6x²+x-1
Answer (1)
Answer:Certainly! Here's the factorization of each trinomial:1. For 3x² - 7x + 4: - First, find two numbers that multiply to 3 * 4 = 12 and add to -7. These are -3 and -4. - Rewrite the middle term using these numbers: 3x² - 3x - 4x + 4. - Factor by grouping: (3x² - 3x) + (-4x + 4) = 3x(x - 1) - 4(x - 1). - Factor out the common binomial: (3x - 4)(x - 1).2. For 4x² + 8x + 4: - Recognize this as a perfect square trinomial. - It factors as (2x + 2)² or simplified, 2(x + 1)².3. For 5x² - 2x - 3: - Find two numbers that multiply to 5 * (-3) = -15 and add to -2. These are -5 and 3. - Rewrite the middle term: 5x² - 5x + 3x - 3. - Factor by grouping: (5x² - 5x) + (3x - 3) = 5x(x -1) +3(x-1). - Factor out the common binomial: (5x + 3)(x -1).4. For 6x² + x –1: - Find two numbers that multiply to 6 * (-1) = -6 and add to +1. These are +3 and –2. - Rewrite the middle term: 6x² + 3x –2x –1. - Factor by grouping: (6x² + 3x) – (2x +1) = 3x(2x +1) –1(2x+1). - Factor out the common binomial: (3x –1)(2x +1).These factorizations simplify the given quadratic expressions effectively.Step-by-step explanation:
