, MAT1511 Assignment 2 (COMPLETE ANSWERS)
2025 - DUE April 2025; 100% TRUSTED Complete,
trusted solutions and explanations.
1. Let P(x) = x6−2x5−x4+x3+2x2+x−2(a) Determine whether
(x−2)is a factor of P(x). (2)(b) Find all the possible rational
zeros of P(x)by using the Rational Zeros Theorem. (2)(c) Solve
P(x) = 0. (4)3. Find a fourth-degree polynomial with integer
coefficients that has zeros 3iand −1, with −1azero of
multiplicity 2. 3.Determine without converting the form and
leave your answer in the form a+bi, where a,b∈R.(i)i21 (i+2)
(i−3)(2)(ii)(1+2i)(3+i)−2+i(4)5. Simplify the following complex
number, without changing the polar form and leave
youranswer in polar form2∠2π333∠3π24∠7π3(6 Let Z = −1−
√ 3i (i) Write Z in a polar form (2) (ii) Use De Moivre’s
Theorem to determine Z 4 . (3) Z and leave your answer in
polar form with the angle in radians (a) Z = 1−i √ 3 2 (5) 2, 5π
4 , 2,− 5π 4 , −2,− π 4 . (3) (b) Convert into rectangular
coordinates: −4,− 13π 6
Problem 1: Let P(x)=x6−2x5−x4+x3+2x2+x−2P(x) = x^6 -
2x^5 - x^4 + x^3 + 2x^2 + x -
2P(x)=x6−2x5−x4+x3+2x2+x−2
(a) Determine whether (x−2)(x - 2)(x−2) is a factor of
P(x)P(x)P(x).
To determine if (x−2)(x - 2)(x−2) is a factor of P(x)P(x)P(x),
we can apply the Remainder Theorem, which states that if
2025 - DUE April 2025; 100% TRUSTED Complete,
trusted solutions and explanations.
1. Let P(x) = x6−2x5−x4+x3+2x2+x−2(a) Determine whether
(x−2)is a factor of P(x). (2)(b) Find all the possible rational
zeros of P(x)by using the Rational Zeros Theorem. (2)(c) Solve
P(x) = 0. (4)3. Find a fourth-degree polynomial with integer
coefficients that has zeros 3iand −1, with −1azero of
multiplicity 2. 3.Determine without converting the form and
leave your answer in the form a+bi, where a,b∈R.(i)i21 (i+2)
(i−3)(2)(ii)(1+2i)(3+i)−2+i(4)5. Simplify the following complex
number, without changing the polar form and leave
youranswer in polar form2∠2π333∠3π24∠7π3(6 Let Z = −1−
√ 3i (i) Write Z in a polar form (2) (ii) Use De Moivre’s
Theorem to determine Z 4 . (3) Z and leave your answer in
polar form with the angle in radians (a) Z = 1−i √ 3 2 (5) 2, 5π
4 , 2,− 5π 4 , −2,− π 4 . (3) (b) Convert into rectangular
coordinates: −4,− 13π 6
Problem 1: Let P(x)=x6−2x5−x4+x3+2x2+x−2P(x) = x^6 -
2x^5 - x^4 + x^3 + 2x^2 + x -
2P(x)=x6−2x5−x4+x3+2x2+x−2
(a) Determine whether (x−2)(x - 2)(x−2) is a factor of
P(x)P(x)P(x).
To determine if (x−2)(x - 2)(x−2) is a factor of P(x)P(x)P(x),
we can apply the Remainder Theorem, which states that if
