Consider the polynomial P(x) = 4x² + 5x³ − 2x² + 5x – 6. (b) What are the possible rational roots of P(x)?

Q: A quadratic polynomial y = 4x2 +7x -3 has roots p and q. Find a quadratic g(x) = x² + ax +B with…

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Q: Consider the polynomial P(x) = 9x³ – 12x2 – 20x +16. Write P(x) as a product of linear factors. You…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find 2) (x) using long division for f(x) = x? + 8x + 16 g(x) = x + 3 The quotient is The remainder…

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Q: 3. Let p(x) = 6xª – 13x³ + 13x² – 2. - (a) Find q(x) such that p(x) = (2x – 1)q(x) using synthetic…

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Q: 12) List the potential rational zeros of the polynomial function. Do not find the zeros. f (x) =…

A: Since given function is f(x) = -3x2-2x+8 Constant term =8 leading coefficient(coefficient of x2) =-3…

Q: Consider the polynomial equation of P(r) = 0 where P(x) = #* – a* – ² – a – - 2. - T (a) What are…

A: The given polynomial is Px=x4-x3-x2-x-2.

Q: A quadratic polynomial y = 4x² + 7x – 3 has roots p and q. Find a quadratic g(x) = x + ax + Bwith…

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Q: 2. Write the polynomial f(x) = 5x-4 in the form f(x) = (x−2)Q(x) + f(2) for some polynomial Q(x).

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Q: f (x) = 6x6 + 13x5 + 3x4 − 2x3 − 30x2 − 56x − 24. (a) Use the Rational Zeros/Roots Test to list all…

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Q: Given a polynomial f(x), if (x − 2) is a factor, what else must be true?  a) f(0) = 2 f b) (0) =…

A: NOTE: Refresh your page if you can't see any equations. . use the remainder theorem to solve this…

Q: Consider the polynomial P(x) = 6x³ – 19x² − x + 24. (i) Find the value of P (−1) (ii) Based on (i)…

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Q: XII. Given two polynomials: A(x) = 12x3 - 4x2 - 3x +1 B(x) = (3x – 1)(5x – 2) – (9x² – 6x + 1) 1)…

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Q: Approximate the roots of the polynomial f(x) = X3 - 7X + 6 using Bolzano method.

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Q: 1. Sketch the polynomial /(x) = (2-x)²(x+1)(x-4)³

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: One factor of f(x) = x^3 –8x^2 – 15x+54 is x - 2. What are the zeros of f(x)?

A: Solution of the equation

Q: Show that f (x) = x2 + 3x−1 and g(x) = 3x3 − 9x + x−2 are rational functions—that is, quotients of…

A: To show: That the functions are rational function: Given: The functions are fx=x2+3x-1 and…

Q: If f(x) is a polynomial of the first degree and a is not equal to B, show that f(x)= f(B)(x-a) -…

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Q: 5) Use long division to find the quotient Q(x) and remainder R(x). P(x) = 6x³ 2x² + 4x - 1 and d(x)…

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Q: Let P(x) be a polynomial of degree 5 with roots 2, – 5 and (3 + i). Write P(x) as a product of…

A: It is given that the roots of 5 degree polynomial are 2,-5,3+i

Q: The quadratic form Q(x) = 3x1? – 7x,² + 4x3? is (a) Negative definite (b) Indefinite (c) Positive…

A: Given a quadratic form we write it in the form of matrix multiplication as…