Find the quotient Q(x) and remainder R(x) when the polynomial P(x) is divided by the polynomial D(x). P(x) = 4x5 + 9x4 − 5x3 + x2 + x − 25; D(x) = x4 + x3 − 4x − 5 Q(x) = R(x) = Use the Factor Theorem to show that x − c is a factor of P(x) for the given values of c. P(x) = 2x4 − 13x3 − 3x2 + 117x − 135; c = −3, c = 3...
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...
4. Let P(x)=x3-5x2+x-5 Factor the polynomial into a product of linear factor some of which may by complex factors. (20pts)
* 5. Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree: 3; zeros: -2 and 2i (a) f(x) = x + 2x² + 4x +8 (c) f(x) = x2 – 2x² + 4x – 8 (b) f(x)= x + 2x2 - 4x + 8 (d) f(x) = x3 – 2x2 - 4x - 8
MAT 121 Final 7. DETAILS 0/2 Submissions Used 40 29 20 Suppose the graph of p(x)=x-10x2+42x-72 is shown above. (a) Determine the unique real root of p from the graph. () Determine a linear factor of p(x) with real coefficients and with leading coefficient 1. (c) Use the linear factor of p(x) above, and long division, to determine an irreducible quadratic factor of p(x) with leading coefficient 1. (d) Determine the remaining two non-real zeros of p. (e) Factor P(x)...
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.)
63 only Using the Factor Theorem In Exercise use synthetic division to show that x is a soluti third-degree polynomial equation, and use the factor the polynomial completely. List all real of the equation. 59. x3 – 7x + 6 = 0, x = 2 60. x3 – 28x – 48 = 0, x = -4 61. 2x3 – 15x2 + 27x – 10 = 0, x = 62. 48x3 – 80x2 + 41x – 6 = 0, x =...
How many and of which kind of roots does the equati f(x) = x3 + 2x2 + 4x + 8 have? A. 2 real; 1 complex B. 3 real C. 2 real; 2 complex D. 1 real; 2 complex
Write the polynomial f(x) as a product of irreducible polynomials in the given ring. Explain in each case how you know the factors are irreducible. 1) f(x) -x* + 2x2 +2x 2 in Z3[x]. 2) f(x)4 + 2x3 + 2x2 +x + 1 in Z3[x]. 3) f(x) 2x3-x2 + 3x + 2 in Q[x] 4) f(x) = 5x4-21x2 + 6x-12 in Q[x)
a webassign.net Section 3.5 - Math 187, section 16373, Summer 1 2020 | WebAssign Get Hamework Help With Chagg Study Chagg.com Factor the polynomial completely P(x) - *3-8 P(x) - Find all its zeros. State the multiplicity of each zero. (Order your answers from smallest to largest real, followed by complex answers ordered smallest to largest real part, then smallest to largest imaginary part.) with multiplicity with multiplicity with multiplicity Need Help? Read It Watch It Master it Talk to...