In Exercises 23–30, factor each expression and simplify as much as possible.
Trending nowThis is a popular solution!
Chapter 0 Solutions
Finite Mathematics
- Exercises 141–143 will help you prepare for the material covered in the next section. In each exercise, factor the polynomial. (You'll soon be learning techniques that will shorten the factoring process.) 141. x? + 14x + 49 142. x? – 8x + 16 143. х2 — 25 (or x? + 0х — 25)arrow_forwardIn Exercises 126–129, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. 126. Once a GCF is factored from 6y – 19y + 10y“, the remaining trinomial factor is prime. 127. One factor of 8y² – 51y + 18 is 8y – 3. 128. We can immediately tell that 6x? – 11xy – 10y? is prime because 11 is a prime number and the polynomial contains two variables. 129. A factor of 12x2 – 19xy + 5y² is 4x – y.arrow_forwardFor Exercises 115–120, factor the expressions over the set of complex numbers. For assistance, consider these examples. • In Section R.3 we saw that some expressions factor over the set of integers. For example: x - 4 = (x + 2)(x – 2). • Some expressions factor over the set of irrational numbers. For example: - 5 = (x + V5)(x – V5). To factor an expression such as x + 4, we need to factor over the set of complex numbers. For example, verify that x + 4 = (x + 2i)(x – 2i). 115. а. х - 9 116. а. х? - 100 117. а. х - 64 b. x + 9 b. + 100 b. x + 64 118. а. х — 25 119. а. х— 3 120. а. х — 11 b. x + 25 b. x + 3 b. x + 11arrow_forward
- Consider the algebraic expression 3 – 15x*. What is the degree of this polynomial? Identify the constant term. Identify the leading coefficient. Identify the leading term.arrow_forwardCompare the answers in Exercises 125 and 126. Based on these results, whatis the factorization of x4 + x2 + 1?arrow_forwardFind the quotient of x3n + 1 and xn + 1.arrow_forward
- In Exercises 130–131, find all integers b so that the trinomial can be factored. 130. 4x? + bx – 1 131. 3x + bx + 5arrow_forwardExpand and simplify. (a) 3(x+6) + 4(2x -5)arrow_forwardIn Exercises 34–37, solve each polynomial equation. 34. 3x? = 5x + 2 35. (5x + 4)(x – 1) = 2 36. 15x? – 5x = 0 37. x - 4x2 - x + 4 = 0arrow_forward
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning