Algebra Demystified 2nd Ed

146 algebra De mystif ieD EXAMPLES Completely factor the expression. 6(x + 1)^2 – 5(x + 1) Each term has x + 1 as a factor. The ...

Chapter 6 FaCtoring and the distributive ProPerty 147 2(x^2 − 6)^9 + (x^2 − 6)^4 + 4(x^2 − 6)^3 + (x^2 − 6)^2 = 2 (x^2 − 6 )^7 ...

148 algebra De mystif ieD PRACTICE Use factoring by grouping to factor the expression. 6xy^2 + 4xy + 9xy + 6x = x^3 + x^2 − x − ...

Chapter 6 FaCtoring and the distributive ProPerty 149 PRACTICE Factor the numerator and denominator, and then write the fraction ...

150 algebra De mystif ieD Simplifying a fraction or adding two fractions sometimes only requires that we factor –1 from one or m ...

Chapter 6 FaCtoring and the distributive ProPerty 151 − − (^10) = 73 x^2 x 4.^98 6 + −− y= x 5.^85 58 xy xy − − = 6.^543 916 x ...

152 algebra De mystif ieD F(first × first) + O(outer × outer) + I(inner × inner) + L(last × last) FFirst First FF ×+()xx 42 ()−= ...

Chapter 6 FaCtoring and the distributive ProPerty 153 ()()xx–+ 34  = (x − 5)(x + 5) = (x − 6)(x + 6) = ()()xx+–^22 = (x + 8)^2 ...

154 algebra De mystif ieD (x + 8)^2 = (x + 8)(x + 8) = x(x) + 8x + 8x + 8(8) = x^2 + 16x + 64 (x − y)^2 = (x − y)(x − y) = x(x) ...

Chapter 6 FaCtoring and the distributive ProPerty 155 EXAMPLES Determine whether to begin the factoring as (x + __ )(x + __ ), ( ...

156 algebra De mystif ieD consider 1 and 12, 2 and 6, and 3 and 4. If both signs in the factors are the same, these are the only ...

Chapter 6 FaCtoring and the distributive ProPerty 157 x^2 + 4x − 21 = x^2 + 13x + 36 = x^2 + 5x − 24 = ✔SOLUTIONS x^2 − 5x − ...

158 algebra De mystif ieD x^2 + 11x + 24: 3 ⋅ 8 = 24 and 3 + 8 = 11 x^2 + 11x + 24 = (x + 3)(x + 8) x^2 – 9x + 18: 3 ⋅ 6 = 18 an ...

Chapter 6 FaCtoring and the distributive ProPerty 159 The shortcut for factoring a quadratic polynomial where first term is x^2 ...

160 algebra De mystif ieD ✔SOLUTIONS x^2 − 4 = (x − 2)(x + 2) x^2 − 81 = (x − 9)(x + 9) x^2 − 25 = (x − 5)(x + 5) x^2 − 64 = (x ...

Chapter 6 FaCtoring and the distributive ProPerty 161 PRACTICE Use the formula to factor the difference of two squares. x^4 − 1 ...

162 algebra De mystif ieD More on Factoring Quadratic Polynomials When the first term is not x^2 , we look to see if we can fact ...

Chapter 6 FaCtoring and the distributive ProPerty 163 EXAMPLE Factor the quadratic polynomial. 4 x^2 – 4x – 15 The possibilities ...

164 algebra De mystif ieD You can see that when the constant term and the coefficient of x^2 have many factors, this list of fac ...

Chapter 6 FaCtoring and the distributive ProPerty 165 x^10 – 2x^5 – 3 = (x^5 – 3)(x^5 + 1) x– 4 – 2x– 2 – 3 = (x– 2 – 3)(x– 2 + ...