For Exercises 105–110, factor the expressions over the set of
In Chapter R we saw that some expressions factor over the set of integers. For example:
Some expressions factor over the set of irrational numbers. For example:
To factor an expression such as x2 1 4, we need to factor over the set of complex numbers. For example, verify that
a.
b.
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Chapter 1 Solutions
ALEKS 360 COLLLEGE ALGEBRA ACCESS
- Exercises 143–145 will help you prepare for the material covered in the next section. In each exercise, factor completely. 143. 2r + 8x? + 8x 144. 5x3 – 40x?y + 35xy2 145. 96?x + 9b²y – 16x – 16y -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_forwardIn Exercises 133–136, factor each polynomial completely. Assume that any variable exponents represent whole numbers. 133. y + x + x + y 134. 36x2" – y2n 135. x* 3n 12n 136. 4x2" + 20x"y" + 25y2marrow_forward
- Rationalize the numerator of x+10 – 100 Paragraph A.arrow_forwardIn Exercises 106–108, factor and simplify each algebraic expression. 106. 16x + 32r4 107. (x² – 4)(x² + 3) - (r? – 4)°(x² + 3)2 108. 12x+ 6xarrow_forwardIn Problems 5–12, tell whether the given rational expression is proper or improper. If improper, rewrite it as the sum of a polynomialand a proper rational expression.arrow_forward
- Compare the answers in Exercises 125 and 126. Based on these results, whatis the factorization of x4 + x2 + 1?arrow_forwardThe figure below shows that 4 one-inch segments are needed to make a 1 × 1 square, 12 one-inch segments are needed to make a 2 × 2 square composed of four 1 × 1 squares, and 24 one-inch segments are needed to make a 3 × 3 square composed of nine 1 × 1 squares. How many one-inch segments are needed to make an nx n square composed of 1 x 1 squares?arrow_forwardMake Sense? In Exercises 135–138, determine whether each statement makes sense or does not make sense, and explain your reasoning. 135. Knowing the difference between factors and terms is important: In (3x?y)“, I can distribute the exponent 2 on each factor, but in (3x² + y)', I cannot do the same thing on each term. 136. I used the FOIL method to find the product of x + 5 and x + 2x + 1. 137. Instead of using the formula for the square of a binomial sum, I prefer to write the binomial sum twice and then apply the FOIL method. 138. Special-product formulas have patterns that make their multiplications quicker than using the FOIL method.arrow_forward
- What is the LCD of 17/6x, 11/3x+3arrow_forwardIn Exercises 112–114, multiply or divide as indicated. x* + 6x + 9 x + 3 112. 3x + x 6x + 2 113. x2 - 4 x - 2 x2 - 1 X - 1 x? - 5x - 24 x2 - 10x + 16 114. x? - x - 12 x? + x - 6arrow_forwardIn Exercises 129–132, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. 129. 9x? + 15x + 25 = (3x + 5) 130. x - 27 = (x – 3)(x² + 6x + 9) 131. x³ – 64 = (x – 4)3 132. 4x2 – 121 = (2x – 11)arrow_forward
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
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