MA1210 College Assignment: Factoring Polynomials And Solving Rational Expressions Week 2 Lab

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Page1MA1210 College Assignment: Factoring Polynomials and SolvingRational Expressions Week 2 LabFactorizing Polynomials and Solving Rational ExpressionsAnswer the following questions and show all your calculations. There are differentmethods forfactoring. All methods involve some sort of trial and error. That’s why it isalways important to check your answer by foiling.1.Factor a trinomial whose leading coefficient is 1.Pick any one of the problems andsolve the trinomial. If the trinomial is prime, state this and explain why.a.x2+8x+15= (x + 3)(x + 5)b.x24x5= (x-5)(x + 1)c.x214x+45= (x-9)(x-5)Answer:Let's go through each trinomial and factor them one by one.1. a. x2+8x+15x^2 + 8x + 15We need to factor thetrinomial x2+8x+15x^2 + 8x + 15.Step 1: The leading coefficient is 1, so the factors of 15 need to add up to 8.Step 2: The factors of 15 are (1, 15), (3, 5), (-1,-15), and (-3,-5).Step 3: The pair that adds up to 8 is 3 and 5.Thus, thefactored form of the trinomial is:x2+8x+15=(x+3)(x+5)x^2 + 8x + 15 = (x + 3)(x + 5)1. b. x2−4x−5x^2-4x-5Now, let's factor x2−4x−5x^2-4x-5.Step 1: The leading coefficient is 1, so we look for factors of-5 that add up to-4.Step 2: Thefactors of-5 are (1,-5) and (-1, 5).Step 3: The pair that adds up to-4 is-5 and 1.Thus, the factored form of the trinomial is:x2−4x−5=(x−5)(x+1)x^2-4x-5 = (x-5)(x + 1)1. c. x2−14x+45x^2-14x + 45

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