2 = 0 x =− Let = u → = x u x 2 ( ) ( ( The zeros of = 2 + 1)2 − 5 + 1) P x x x + 8u = 0 u 2 (u − 3 are + 8) = 0 u − 3 and 2. The of the graph of x-intercepts P 2 = 0 or + 8 = 0 u u and 2. ( ) = = −8 0 x x = H x = not real x = 02 = 0 are − 3 0 x 2 80. = −8 u )2 (1 ) 3(1 − + 5 − + x x Check: (0) = 0 + 8 0 = 0 f 2 = 0 is 0. The (1 )2 x Let = − u x 2 only ( ) = + 8 f x x The only zero of = − → 1 u x (3u (u + 2) + 1) = 0 3u + 5u + 2 = 0 2 of the graph of is 0. x-intercept f + = 3u 2 0 + 1 = 0 u or 2 =− u = −1 u 3 1 − = −1 x − = − 1 2 x 3 = 2 x = 5 x 3
x = 0 2 =− Let u = 2 x → u = x The zeros of P ( x ) = 2 ( x + 1)2 − 5 ( x + 1) − 3 are u 2 + 8u = 0 u (u + 8) = 0 − 3 and 2. The x-intercepts of the graph of P 2 u = 0 or u + 8 = 0 80. are − 3 2 and 2. H ( x ) = 0 x = 0 x = 02 = 0 u = −8 x = −8 x = not real 3(1 − x )2 + 5 (1 − x ) + 2 = 0 Check: f (0) = 0 + 8 0 = 0 Let u = 1 − x → u 2 = (1 − x )2 The only zero of f ( x ) = x + 8 x is 0. The only 3u 2 + 5u + 2 = 0 (3u + 2) (u + 1) = 0 x-intercept of the graph of f is 0. 3u + 2 = 0 or u + 1 = 0 2 u =− u = −1 3 1 − x = −1 1 − x = − 2 3 x = 2 x = 5 3