Let P(x) = 2x4 + 2x3 + x² + 5x-10. a) b) Use the Rational root theorem to find all the possible rational root of P(x) = 0. Use the bounds theorem to find an upper bound for the modulus of the roots of P(x). Does this eliminates any answer from part (a)? c) | Find all roots of P(x) = 0 and decompose P(x) according to its factors.

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: 16) Given the function f(x)=2x –1lx² +22x–15, find all the complex roots, given that 2-i is a root.…

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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: Let 0 be a root of the polynomial x³ + 3x + 7. Prove that 0 is prime in Q(0).

A: We will use the basic knowledge of polynomials and rings to answer this question properly, in…

Q: Use two methods: 1) the rational root theorem and Descartes' rule of signs to find them. 2) Use…

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Q: 3. a) For the polynomial function P(x) = 2x- 7x? + 4x + 4, could there be exactly 1 real-valued…

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Q: List all possible rational zeros, find all rational zeros, and factor f(x). 3 f(x) =x-3x-33x+35 13…

A: Given: fx=x3-3x2-33x+35

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

A: Given polynomial is P(x)=4x4+5x3-2x2+5x-6 The possible rational roots of P(x) are determined as…

Q: Consider the following cubic polynomial function: p(x) = 2x32x29x - 5 a) How many zeros does this…

A: a)  3b)  Nc)  -14Explanation:Thank you 😊

Q: #11

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Q: Determine equation of the polynomial function in factored form and IN THREE POSSIBLE WAYS if “A…

A: Given Information:The quartic function with real zeroes only at  and a point  on its graph.To…

Q: The possible rational roots of f(x) = 5x³-82² - 4x +3 are = (Use "+" to indicate the symbol. So…

A: Rational roots theorem

Q: 10. Show that the polynomial p(x)=x²-3x³-x² - 4x-20 has at least two distinct roots (Hin use the…

A: We have given,   f(x) = x4 - x2 - 4x - 20

Q: The figure shows that graph of p(x) = x* – 7x³ – 9. Use the intermediate value theorem to prove that…

A: The graph of the function px=x4-7x3-9 is as follows:

Q: Determine a polynomial p(x) of degree 2 having zeros −5 and 7

A: The problem is asking us to find a polynomial of degree 2 that has zeros at -5 and 7. In other…

Q: 2. The possible rational zeros of the function p(x)=x³+ 2x²+ 2x+ 6 are: (a) ±1#2,±3 (b) +1,+2,+6 (c)…

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Q: List the possible rational zeros of the function using the Rational Roots Theorem. f(z) = 3x3+ 9x2+…

A: Explanation of the answer is as follows

Q: 14) For a polynomial with Degree 3; an-5; zeros 2, i, and -i a) Find the complete factored form of…

A: Given:Degree of the polynomial = 3Real coefficient an = 5Zeros of the polynomial are 2, i and -i.

Q: 20-R] [CLO 22] Let q be the polynomial function given by the formula q(x) = 3x5 − 6x3 + x2 − 6.…

A: To apply the rational root test to the polynomial q(x) = 3x^5 − 6x^3 + x^2 − 6, we need to consider…