(2) Factor. Simplify further where appropriate. For (d) and (e), indicate what values of the variable make the expression undefined.
(a) 42t2 - 6yt - 96xt
(b) x - 2x2
(c) (5a + b)(a - b) - 11b(a - b)
(d) y2 + y
-------
y + 1
(e) 4x2 + 8x
---------
2x3
SOLUTION:
(a) 42t2 - 6yt - 96xt
6t(7t - y - 16x)
(b) x - 2x2
x(1 - 2x)
(c) (5a + b)(a - b) - 11b(a - b)
(a - b)[(5a + b) - 11b]
(a - b)(5a -10b)
(d) y2 + y y(y + 1)
------- = --------- = y
y + 1 (y + 1)
To find the values of y that make the expression undefined, the denominator
must NOT equal zero.
Thus, (y + 1) not equal to 0
(y) not equal to (-1)
The expression is undefined when y = (-1).
(e) 4x2 + 8x 4x(x + 2) 2(x + 2)
--------- = ---------- = ---------
2x3 2x3 x2
The expression is undefined when the denominator is zero, so in this
case, x can not be equal to 0. If x = 0, then the expression is
undefined.