1. Is x³ - 2√5x + x a polynomial? If not, state a reason. 2. Is -2020x a polynomial? If not, state a reason. 3. Is x⅔ + 3x + 1 a polynomial? If not, state a reason. 4. Is 1/x² + 2/x³ + r/x4 a polynomial? If not, state a reason. 5. Is π a polynomial? If not, state a reason. 6. Is 3x√2 + √3x² a polynomial? If not, state a reason. 7. Is x³ +2x + 1 a polynomial? If not, state a reason. 8. Is -2x-3 +x³ a polynomial? If not, state a reason. 9. Is 1 - 4x² a polynomial? If not, state a reason.

Q: 3. List all the possible rational roots of the polynomial. p(x) = 2x5+ 21x-42x +5x3 + 93x2-7x + 50…

A: Explanation of the solution is given below...

Q: The polynomial p(x) = -2x°+ 3x +4 is given. Which conclusion is valid if p(1)

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Q: Given a polynomial that has zeros of -4,9i, and -9i has a value of 492 when x = -1. Write polynomial…

A: Given that the polynomial that has zeros of −4, 9i, and −9i, we can say that x = -4 => x + 4 = 0…

Q: Which statement about k (x) x² -2x + 15 is true? %D - O The zeros are -3 and 5 O The zeros are -5…

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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: (a) If we divide the polynomial P(x) by the factor x - c and we obtain a remainder of 0, then we…

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Q: a. Given the set {-3x3 + 2x2 + x – 2, –3 z3 + 2x² + x – 2,2 a3 – 2 22 + 1, x³ + 3x² – 3x + 2} write…

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Q: 4. Answer the following questions: a. For the given polynomial, find: x3 + 2x + a 7 -x2 - x6 2…

A: Also, the value of a is 8. Therefore, the Polynomial becomes,

Q: what is the coefficient of x^4 in (2x+1)^5

A: 2x+15 Comparing with a+bn, we get a=2x,  b=1  &  n=5

Q: 5. Suppose you use polynomial long division to divide p(x) by q(x), and after doing your…

A: We know that, the number which we divide is called the dividend. The number by which we divide is…

Q: In Exercises 16-33, factor completely, or state that the polynomial is prime. 16. 14x3 – 15x² 17.…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Find the quotient and the remainder when the first polynomial is divided by the second. (a). x3 +…

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Q: Consider polynomial P(x) = x³ +x² – 10x – 10. 1. Is x+1 one of the factors of P? Explain.

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Q: ow by contradiction that if 5x2+ 3 is irrational, then x is irrational. -

A: Proof by contradiction

Q: (a) Construct a table containing the values of the fourth- degree polynomials f(x) = 2x", g(x) = 2r…

A: Given: The functions, f(x) = 2x4g(x) = 2x4-5x2+1h(x) = 2x4+5x2-1k(x) = 2x4-x3+2xx = ±20, ±40, ±60

Q: (a) If we divide the polynomial P(x) by the factor x - c and we obtain a remainder of 0, then we…

A: We have to fill the blanks with appropriate words.

Q: Consider polynomial P(x) = x³ + x² – 10x – 10. 1. Is x + 1 one of the factors of P? Explain.

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Q: 2. Which of the following are all the possible rational zeros for the polynomial x - 3x + 27x - 8?…

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Q: 10. Determine whether the first polynomial in P3(R) can be expressed as a linear combination of the…

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Q: 413 71 + 2 This is a rational expression because the denominator contains a variable. 4 This is a…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: 1. The number of courses that Felix takes in this cycle is numerically equal to the number of prime…

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Q: When P(x) is divided by (x-1), the remainder is 3. When P(x) is divided by (x+1), the remainder is…

A: When P(x) is divided by (x-1) then the remainder is 3. ⇒ P(1) = 3 When P(x) is divided by (x+1) then…

Q: 1. If we divide the polynomial P by the factor x obtain the equation P(x) = (x – c)Q(x) + R(x), then…

A: To fill: The blanks of the statement "Qx is _______, and Rx is the _________." Given: If polynomial…

Q: . If we divide the polynomial P by the factor x  c and weobtain the equation P1x2  1x  c2Q1x2 …

A: If we divide the polynomial P by the factor x-c and we obtain the equation Px=x-cQx+Rx, then we say…

Q: (a) If we divide the polynomial P(x) by the factor x – c and we obtain a remainder of 0, then we…

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Q: The negation of “For all real numbers x, if x > 2 then x^2>4” is “For all real numbers x, if x > 2…

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Q: A polynomial P ( x ) with real coefficients has 5 + 9 i as a zero. What other number must be a zero…

A: Comples zeroes of polynomial always come with conjugate pair. For example if a + b i is zero then a-…

Q: What set of x and y creates the Pythagorean triple 12,35,and 37? Use the polynomial identity…

A: We need to use the polynomial identity: (x2+y2)2 = (x2-y2)2 + (2xy)2 to find values of x and y which…

Q: 5. Given the polynomial P(x) = 3x + kx? + mx + 12 has a known factor of (x-3). When P(x) is divided…

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Q: 12) Consider the polynomial P(x) = 2x + kx? + 7x - 6 %3D a) Find the value of k, such that when P(x)…

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Q: Which of the following statements is not true regarding the division of polynomials?       a)…

A: Polynomial division is similar to the way numbers are divided, The method of division in both cases…

Q: If we divide the polynomial P(x) by the factor x − c and we obtain a remainder of k, then we know…

A: Remainder theorem states that if we divide a polynomial by x-a then the remainder will be fa. Here,…

Q: (a) If we divide the polynomial P(x) by the factor x - c and we obtain a remainder of 0, then we…

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Q: Which statement about 6x + 7x – 10 is true? O One of the factors is (x + 2). O One of the factors is…

A: To factorise ax2+bx+cwe have to break 'b' in such a waythat sum is 'b' & the product is ac.

Q: What are all the possible rational roots of the polynomial )= -3r+x-37 1.3 B 1.-1.3.-3 1.-1.2.-2. 3.…

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Q: Which of the following is not a factor of x^3 + 5x^2 - x - 5? * 5 puntos x + 1 x - 5 x + 5 x - 1…

A: Given the polynomial

Q: ) List all the possible rational zeros of flx) = 2r - 5x + 2x + 6 A) 2, ±3, 26 * 21, 2, 23 ±1, C)…

A: Topic = Algebra

Q: What is the zero of r (x) x +12 ? %3D O12 O 9/3 O None of the above /3

A: We put polynomial equal to 0 and find out the value of x. The value of x is our zero of r(x).

Q: 2) If a + bi is the remainder when P(x)=x²1 - 8x5 + x is divided by x +i, then a + b = A) -8 B) 6.…

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

Q: Assume that the polynomial 7? + bx +c = 0 in which b, cE Z, has two integer solutions. Which one of…

A: We have to equation as - x2 + bx + c = 0.......(1) The above equation (1) is a quadratic equation…

Q: The polynomial p(x) = - 2x ^ 3 + 3x + 4 is given. Which conclusion is valid if p(1) = 5

A: Given ,  The polynomial  p(x) = -2x3 + 3x + 4  We have to find valid conclusion if p(1) = 5

Q: If P ( x ) is a polynomial with real coefficients that has − 9 − 5 i as a zero, what other number…

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Q: If we divide the polynomial P by the factor x - c and we obtain the equation P(x) = (x – c)Q(x) +…

A: we know that if we divide the polynomial px by the factor x-c and we obtain the equation…

Q: 2. (a) If we divide the polynomial P(x) by the factor x - c and we obtain a remainder of 0, then we…

A: Consider two polynomials f(x), g(x) such that degree of g(x) is less than or equal to the degree of…

Q: Determine whether the second polynomial is a factor of the first. 4x +3x+34; x-4 Select the correct…

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Q: One zero of P(x)=x3+ 4x2- 9 is x= -3. The other two zeros are x =a±√b/ c. The exact values of a,b…

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Q: Q.18 If x– 1 and x + 2 are factors of x +10x + ax+b, then find the values of a and b. If x = 2 and x…

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Q: 7x-3 + 9x – 13 is not a polynomial because the coefficient of the second term is 9. x5y3 – 5x2y2 +…

A: Solution as follows

Q: 9. State the leading coefficient of the polynomial. (Hint: Be sure it's in standard form first.) *…

A: 9. The polynomial is given by 36x3-8x4-32x5+9x2 To determine : The leading coefficient of the…

Q: 5. When the polynomial 3x + ax? +bx-9 is divided by x-2 the remainder is – 5. When it is divided by…

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Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.