4. Let P(x)=x3-5x2+x-5 Factor the polynomial into a product of linear factor some of which may...
A polynomial P is given. P(x) = x3 - 2x2 + 4x - 8 (a) Factor Pinto linear and irreducible quadratic factors with real coefficients. P(x) = (x+2) (x²+4) (b) Factor P completely into linear factors with complex coefficients. P(x) = (x + 2)(x2+4) Need Help? Read It Watch It
Factor the polynomial f(x). Then solve the equation f) o. 10) f(x) x3+5x2- 9x-45 State the domain of the rational function. (6 points) 11) g(x) =ー2 x +2 Given that the polynomial function has the given zero, find the other zeros. 12) f(x)=x3-4x2 + 9x-10:2
4-Factor the polynomial x3 - 7x² + 16x – 12 completely if x – 3 is one of the factors. (5 pts.) 5-Solve the equation: 2x* - 5x3 - 2x2 + 11x – 6= 0 (5 pts.)
A polynomial P is given. P(x) = x3 + 64 (a) Find all zeros of P, real and complex. (Enter your answers as a comma-separated list. (b) Factor P completely A polynomial P is given. P(x) = x364 (a) Find all zeros of P, real and complex. (Enter your answers as a comma-separated list. Enter your answers as comma-separated list.) -4.2 +2i 3 .2-2i 3 X = (b) Factor P completely. P(x) (x-4)(x - 2+ 2i/ 3 ) (x -2-2/V3...
Let p(x) be the polynomial The companion matrix of p(x) is the n x n matrix 1 1 n-2 .. -a-a0 cp) = 10 1 0 Find the companion matrix of p(x) - x3 + 5x2 - 2x 15 and then find the characteristic polynomial of C(p). C(p) det(C(p) Xr)-
2. Consider the polynomial p = x3 + x +4 € Z5 [2]. Let q = 3x +2 € Z5 [2]. (a) Is p reducible or irreducible? Prove your claim. (b) Are there any degree 2 polynomials in [g],? Explain. (c) List all degree 3 polynomials in [g]p. (d) (ungraded for thought) How many degree 4 polynomials are in (q),? Degree 5?
How to find quadratic factor? Let p(x) be a real polynomial of degree 4, You are given that p(-7-5 i) = 0. the box below using Maple syntax. (Don't forget to use for mulitplication.) A real quadratic factor of p(x) is Let p(x) be a real polynomial of degree 4, You are given that p(-7-5 i) = 0. the box below using Maple syntax. (Don't forget to use for mulitplication.) A real quadratic factor of p(x) is
previous problem Problem 5 Let p.) be a polynomial satisfying the same constraints as in the previous problem and let (2) be given as in the preceding problem. Show that p.) = r(c)(c) for some polynomial r(c). Hint: you can use the fundamental theorem of linear algebra and the generalized product rule for derivatives Problem 4 Prove that the polynomial q(x) given by g(x) = II (2 – x;) satisfies the linear constraints 9(wo) = 0, d'(x0) = 0, ......
3) Write a polynomial f(x) that meets the given conditions. Answers may vary. 3) Degree 2 polynomial with zeros 212 and -222 A) S(x) = x2 + 472x+8 B) f(x) = x2-8 9 S(x) = x² + 8 D) S(x) = x2-11/2x+8 4) Degree 3 polynomial with zeros 6, 21, and -2i A) S(x) => x3 + 6x2 + 4x + 24 f(x)= x2 - 6x2 + 4x - 24 B) /(x) = x2 - 6x2 - 4x + 24...
Let x = [X1 X2 X3], and let T:R3 → R3 be the linear transformation defined by x1 + 5x2 – x3 T(x) - X2 x1 + 2x3 Let B be the standard basis for R3 and let B' = {V1, V2, V3}, where 4 4. ---- 4 and v3 -- 4 Find the matrix of T with respect to the basis B, and then use Theorem 8.5.2 to compute the matrix of T with respect to the basis B”....