Math 1011 Worksheet 1

Math 1011 Worksheet 1Name:1. Show that the following formulas are true.(a) x 3 − y 3 = (x − y)(x 2 + xy + y 2 )(b) x 3 + y 3 = (x + y)(x 2 − xy + y 2 )2. Factor the following polynomials.(a) 2x 4 − 16x(b) 2x 4 − x 3 + 54x − 27(Hint: For part (a), start factoring, then use the previous exercise. For part (b), trygrouping terms first.)1

3. Find all values of c so that the polynomial x 2 + cx − 14 can be factored.Recall that the product of two numbers is zero when at least one of them is zero. Insymbols, a · b = 0 if and only if a = 0 or b = 0 (or both). We can use this fact, along withfactoring, to solve polynomial equations.4. Solve the following polynomial equations.(a) x 2 − 5x + 6 = 0(b) 6x 3 + 27x 2 = 15x5. Suppose a company sells shirts for $40 each. If it costs 1 2 x2 + 800 dollars to producex shirts, how many shirts must the company sell in order to break even?2