Question

7. [1pt] Without using a calculator, completely factor the following over C: 235 + 3x4 + 8x3 + 11x2 - 4 Answer. 2(x - 1/2)(x + 1)(x + 2i)(x - 2i)

Please answer all of the question completely and correctly. Show all work and your work must match the highlighted answer provided

Answer 1

is we Sol Altion : p= Qxe5 + 3364 + 8 x3 + 11 12 This polynomial of degree 5. Misc Ralional Root test. Rational Root Test dells you that If the polynomial national zero then it must a fractiona nehere factor o troiling constant and faclor of leading coefficient [P(-1) = 0 -> (36+1) is root of P has a be P P is q q is a Divide P (20) with (2+1) we get 21 3 2 + 3x4 + 8x² + 118² - 4 (at) 2x + x + 70 tuu - 4 q (a) q ( =) O (2+(-1/2) (0) (ov) (x - 12) is another robot 2. 4 (22-12.) 230 828 ។ - x3 + x3 + 7x2 + 44-4 (2+1° + 221 + 8x +8 g(x) 2X² + 7x2 + 40-4 3 20² 1² + 421 - 4 Sa? 80² 48 84 - 4 821-4 g (-1) = 0 (at is also root

2 s(n) 1x +4+ + J (2) (+1) 22 + 4 = 0 0 S(x) = and x=-zi zi 20 = z Answer and two It has (22-1/2) (H+1} (x+2i) (0-21) 3 real roots imaginary roots. complex imaginary