Unit 3 Practice Test Review. Page 9 (back) 5) List all possible rational zeros of this polynomial: 5x 4 – 31x 3 + 11x 2 – 31x + 6 p  1, 2, 3, 6 q  1,

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Presentation transcript:

Unit 3 Practice Test Review

Page 9 (back) 5) List all possible rational zeros of this polynomial: 5x 4 – 31x x 2 – 31x + 6 p  1, 2, 3, 6 q  1, 5 p  1, 2, 3, 6, 1/5, 2/5, 3/5, 6/5 q

Page 9 (front) 4) List all possible rational zeros of this polynomial: -2x 3 + 5x 2 + 6x + 18 p  1, 2, 3, 6, 9, 18 q  1, 2 p  1, 2, 3, 6, 9, 18, 1/2, 3/2,9/2 q

Page 9 back 2) Determine if the binomial is a factor of the polynomial P(x) = x 3 + 5x 2 +7x + 9; x  No when synthetically dividing with -1, the remainder is 6 not 0; so x + 1 is not a factor.

Page 9 (back) 4) x 3 + x 2 – x + 15 = 0; is 1 – 2i is a zero? 1 – 2i| – 2i 1 2 – 2i (1 – 2i )(2 – 2i ) 2 – 2i – 4i + 4i 2 -2 – 6i 1 – 2i| – 2i -2 – 6i – 2i -3 – 6i 0 Yes, when synthetically dividing with 1 – 2i, the remainder is zero; so 1 – 2i is a zero.

Page 9 (back) 9) If -1/3 is a zero of h(x) = 3x 3 – 2x 2 – 61x – 20, find the other zeros. 3x 3 – 2x 2 – 61x – 20 -1/3 | x 2 – 3x – 60 = 0 3(x 2 – x – 20) = 0 3(x – 5)(x + 4) x = 5, -4

Page 9 (front) 9) x 4 + 2x 3 – 4x –4; -1 + i is a zero -1 + i| i 1 1 +i (-1 + i )(1 + i ) -1 – i + i + i i| i -2 2 – 2i I – 2i 0 (-1 + i )(-2 – 2i) i - 2 i - 2 i i| i – 2i 0 -1 – i i x 2 – 2 = 0 x = ±  2

Page 9 (front) 7) Find all zeros x 4 – x 3 – 10x 2 + 4x | ↓ x 3 – 3 x 2 – 4x + 12 = 0 x 2 ( x – 3 ) – 4 (x – 3 ) ( x – 3 ) (x 2 – 4 ) (x – 3 ) ( x – 2 ) ( x + 2) y x

Page 9 (back) Find all zeros 5x 4 – 31x x 2 – 31x  /5   0   0  5x = 0 5(x 2 + 1) = 0 x 2 = -1 x = ± i x = 6, 1/5, ± i 5(x + i)(x – i)(x – 6)(x – 1/5)

Page 9 (front) 8) Find all zeros 18x 3 + 3x 2 – 7x – 2 p  1, 2 q  1, 2, 3, 6, 9, 18 p  1, 2, ½, 1/3, 2/3, 1/6, q 1/9, 2/9, 1/18 18x 3 + 3x 2 – 7x – 2 -½ | ↓ x 2 – 6x – 4 = 0 2(9x 2 – 3x – 2) = 0 2(3x + 1)(3x – 2) x = -1/2, -1/3, 2/3 2(3x + 1)(3x – 2)(x + ½)