Question

Part A: Factor 5x2a2 − 19xa2 − 4a2. Show your work. Part B: Factor x2 + 14x + 49. Show your work. Part C: Factor x2 − 100. Show your work.

Answer 1

Part A: First, we factor out a^2 to obtain: a^2 [5x^2 - 19x - 4] = a^2[(5x+1)(x-4)] Part B: By inspection, we can use the factors (x+7)(x+7). To check that we have indeed chosen correctly, we will multiply our factors to obtain x^2 + 7x + 7x + 49 = x^2 + 14x + 49 = 0, which is correct. Part C: Again, we can use trial and error and try the factors (x+10)(x-10). Multiplying throughout, we obtain x^2 + 10x - 10x - 100 = x^2 -100.