Give an example of each of the following.a. A simple linear factor________________b. A repeated linear factor________________c. A simple irreducible quadratic factor________________d. A repealed irreducible quadratic factor

Problem 2ESolution:-Step1a. A simple linear factordefinition: linear factor 1) words: “linear factor with root r ” 2) usage: r is a some real number 3) meaning: the expression ( x r) Example The polynomial f(x)= can be written as a product of linear factors, f(x)=(x+1)(x-1)(x-2) . Step2b. A repeated linear factorExample 2x+2=Ax-A+bAt A=2-A+B=2-2+B=2B=2+2=4 Step3c. A simple irreducible quadratic factorExample I =First, complete the square: + 4x + 7 = + 3. Thus I = In the first of these two integrals, the numerator x is not a constant multiple of the derivative 2(x + 2) of the denominator, so substitution does not work. Substitute for the quantity in the...