USE the synthetic method of division to divide the polynomial f(z) = 2 – 32 by d(r) %3D

Q: 1. Determine the number of degree and the end behaviours of the polynomial y = (x + 5)(x − 1)(x +…

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Q: Use the remainder theorem and synthetic division to find the value of f(3) if f(x) =x³ – 6x² + 13x –…

A: Topic = Algebra

Q: For the polynomial function ​f(x)=5x4−4x3+44x2−36x−9​,   ​a) Find the rational zeros of​ f(x), and…

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Q: Find a, b, c E R such that the polynomial f(x) = x³ + ax? + bx + c is divisible by g1(x) = x + 2 and…

A: The remainder theorem says that when a polynomial px is divided by x-a. The remainder is obtained as…

Q: For the cubic polynomial function f(x) = ax' + bx + cx + d, find a, b, c, and d so that 0 is a…

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Q: 9. For the polynomial f(x) = x(3x + 1)(x – 2)², determine the leading coefficient, leading term,…

A: Given: fx=x3x+1x-22 Now solve the parenthesis we get, ⇒fx=3x4-11x3+8x2+4x                    ...(1)…

Q: Find a, b, c E R such that the polynomial f(x) = x³ + ax? + bx + c is divisible by g1 (x) = x + 2…

A: The given question is related with polynomials. Given that,                  fx = x3 + ax2 + bx + c…

Q: What is the degree and lead coefficient of the following polynomial? f(z) =−+52 = −x + 5x² − 6x³ +…

A: We have fx=-x+5x2-6x3+10 This can be written as: fx=-6x3+5x2-x+10 The degree is the highest power…

Q: Find the remainder when f(x) = x7 + 3x5 + x - 1 is divided by x2 +1 in Z5[x].

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Q: Given two polynomial functions f(x) = x° – 32x – 6 | and g(x) = x – 6 use synthetic division to find…

A: By synthetic division

Q: Find the second-degree Taylor polynomial for f(x) = 3x? – 4x + 2 about a = 0. %3D P2(x) = %3D What…

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Q: Let f(x) be a polynomial with real coefficients. The polynomial f(x) leaves the remainder 2x +1 when…

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Q: 15. If the zeros of the polynomial x²+px +q are double in value to the zeros of 2x²- 5x -3, find p…

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Q: Consider the polynomial h with h' (x) = (x – 5)³(x – 3)². Use the definition of an inflection point…

A: We will solve the problem.

Q: Given the polynomial function f(x), find the rational zeros, then the other zeros (that is, solve…

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Q: If the result of a polynomial division is 2x 3 − 4x 2 − 5x + 23 x + 2 , make at least three…

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Q: When a real zero x = a of a polynomial function f is of even multiplicity, the graph of f ________…

A: In the factored form of polynomial equation, the number of times a factor appears is called…

Q: Consider the division f(x) ÷ (x – k) where f(x) = (x + 5)²(x – 5)(x + 6)³. %3D (a) What is the…

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Q: Let f(x) = x' + 2x + 4 and g(x) - 3x + 2 in Z,[x]. Then, upon dividing f(x) by glx), we get 7- The…

A: I am solving part7 & part8 as you mentioned.

Q: Find a polynomial of degree 3 that has zeros of 3,-4, and 5, and where the coefficient of x2 is 8. O…

A: Given that the zeros are 3, -4 and 5. So the factors of the polynomial is (x-3), (x+4) and (x-5)…

Q: Find the critical points, A and B, of the following polynomial (with A<B). f(x)=2x3-294x+6 A= ?…

A: The given polynomial is fx=2x3-294x+6.

Q: Use the remainder theorem to find the remainder when f(x) is divided byx-C. f(x) =x* +8x + 12x; x+1

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Q: 1 is a zero of the polynomial P(x)= x³ – 3x* + 7x³ – 13x² + 12x – 4 of multiplicity (а) 3 (b) 5 (c)…

A: Let's find x value.

Q: Use synthetic division to factor f(x) 3 5x – 22x + 56 given f(2) = 0 -

A: Given function When x=2 the value of f(x) is 0 2 is the zero for f(x). Use 2 for synthetic division

Q: Write a polynomial, P(x), in factored form given the following requirements. Degree: 4 Leading…

A: Given, p(x) has Degree: 4 Leading coefficient 1 Zeros at (5,0), (−2,0) and (−3,0) y-intercept at…

Q: Use the Remainder Theorem to evaluate the polynomial function. R(x) = x3 − 2x2 + 3x − 5; R(4)

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Q: Use synthetic division to show that (x+6) is a factor of f(x) = 2x^3 + 11x^2 -21x – 90, show all…

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Q: Express the polynomial x3 + 2x + 3 EZŞ[x]as a product of irreducible polynomials of Z5[x].

A: Explanation of the answer is as follows

Q: (a) What is the degree of Q(7, V3) over Q ? Justify your answer. Is the polynomial X - 5 € QIX)…

A: Degree of extension- Let E be an extension field of a field F i.e. F is a subfield of E, also E is a…

Q: 4. Use synthetic division to show that c is a zero of the given polynomial function. a. P(x) =x'-4x²…

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Q: Given the polynomial: f (x) = 2x° + mx* – 40x° + nx² + 218x – 168 And that two of the roots are x= 1…

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Q: Consider the polynomial h with h'(x) = (x – 5)³(x– 3)². %3D Use the definition of an inflection…

A: we know that a point of inflection is found where the graph of a function changes concavity. To find…

Q: Consider the polynomial P(x) = x² + 3x³ − 2x² − 3x +2. (a) Determine another polynomial Q equivalent…

A: We will use the basic knowledge of Horner's method and logic to answer all three parts of this…

Q: 12. The second-degree Maclaurin polynomial for f(x)=vx+9 is 3+ x² If this 6 108 polynomial is used…

A: The Maclaurin polynomial for f(x)=x+9is 3+x6-x2108 To approximate 8, substitute -1 for x in the…

Q: For the cubic polynomial function f(x) = : ax³ + bx² + cx + d, find a, b, c, and d so that 0 is a…

A: Solution :fx=ax3+bx2+cx+d f0=2  givend=2   ... 1critical number :f'x=0f'x=3ax2+2bx+c3ax2+2bx+c=0c=0…

Q: Suppose p(x) is a cubic polynomial that shares two of its roots with f (x)=2x² – 5x+3, has the same…

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Q: 4. Use synthetic division to show that c is a zero of the given polynomial function. b. P(x) =2x³ –…

A: Solution is given below:

Q: For a polynomial equation P(x) = 0, if P(x) is not factorable, then P(x) = 0 has no real roots.…

A: For a polynomial equation P(x) = 0, if P(x) is not factorable, then P(x) = 0 has no real roots.

Q: 4) Make up a problem which determines the lowest real root of the fourth degree polynomial (you are…

A: The objective is to make a problem that determines lowest real root of fourth degree polynomial…

Q: if xo = 2, x1 = 3 and x2 = 4 the second degree %3| polynomial for f(x) = using Lagrange…

A: Given function is f(x)=12and the nodes are x0=2, x1=3 and x2=4. We have to find second degree…

Q: 3. Do you agree with the statement that “ cubic functions must have at least 1 x-intercept but not…

A: Given:  To show “ cubic functions must have at least 1 x-intercept but not more than 3". To prove…

Q: Evaluate when x = 1 by using the Remainder Theorem. 31. f(x)=x -5x² +6x- 3 32. g(x)=2x –3x² +5x+3…

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Q: Use the factor theorem to find the polynomial of degree 3 having zeroes x = -4, x = 1 - i, and X = 1…

A: A zero of a function is a value in its domain for which the function takes the value 0. A polynomial…

Q: Given that 5x - 2is a factor of polynomial functions f(x) kx- bx + 2k, %3D determine the ratio k: b…

A: Given that 5x-2 is a factor of polynomial functions f(x)=kx2-bx+2k.

Q: 8) For the polynomial function P(x)=x°-x* -2x³ | a) Determine its end behavior as x→0, P(x)→ as…

A: Since you have posted multiple questions we will solve the second question for you. If you want any…

Q: h(x) = x³ + 5x² - 4x-20 %D

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Q: For the cubic polynomial function f(x) = ax³ + bx² + cx + d, find a, b, c, and d so that 0 is a…

A: Solution of given question is written in below steps.

Q: Use synthetic division to find the result when x + 2x2-11a + 24 is divided by x +5. If there is a…

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Q: The value of f(3) for the polynomial f(x)=x3+x2-5x+3 is 24. What does this mean in terms of…

A: Given:  f(x) = x3+x2-5x+3 Now we have f(3) = 24