Chapter 6 FaCtoring and the distributive ProPerty 165x^10 – 2x^5 – 3 = (x^5 – 3)(x^5 + 1)
x– 4 – 2x– 2 – 3 = (x– 2 – 3)(x– 2 + 1)
x2/3 – 2x1/3 – 3 = (x1/3 – 3)(x1/3 + 1)
x^1 – 2x1/2 – 3 = (x1/2 – 3)(x1/2 + 1)
For any nonzero power, xx^2 ⋅PowerP−− 23 ower factors as ()xxPowerP−+ 31 ()ower. In
general, we factor the expression ax^2 ⋅PowerP++bxower c in the same way that we
factor ax^2 ++bx c, except that we work with xPower instead of x.EXAMPLES
Factor the expression.4 x^6 + 20x^3 + 21 = (2x^3 + 3)(2x^3 + 7)
x2/3 – 5x1/3 + 6 = (x1/3 – 2)(x1/3 – 3)
x^4 + x^2 – 2 = (x^2 + 2)(x^2 – 1) = (x^2 + 2)(x – 1)(x + 1)
xx – 28 – = xx^11 – 28 //^21 – = ()xx^21 – 42 ( /^2 + )) = ()()xx – 42 + xx – 214 – 52 = xx^12 //– ^14 – 15 = ()xx^14 //– 5 (^14 ++ 35 ) = ()()^44 xx – + (^3)
PRACTICE
Factor the expression.
- x^4 − 3x^2 + 2 =
- x^10 − 3x^5 + 2 =
- x2/5 − 3x1/5 + 2 =
- x−6 − 3x−3 + 2 =
- x1/2 − 3x1/4 + 2 =
- x^4 + 10x^2 + 9 =
- x^6 − 4x^3 − 21 =
- 4x^6 + 4x^3 − 35 =
- 10x^10 + 23x^5 + 6 =
- 9x^4 − 6x^2 + 1 =
- x2/7 − 3x1/7 − 18 =
- 6x2/3 − 7x1/3 − 3 =
- x1/3 + 11x1/6 + 10 =
EXAMPLES
Factor the expression.PRACTICE
Factor the expression.