In Exercises 1–16, divide using long division. State the quotient, q(x), and the remainder, r(x). 18x4 + 9x3 + 3x2 /3x2+1

Q: Under what special condition can the synthetic division method be used? Create your own example of…

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Q: +2x-2 h(x) 5x +

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Q: Use synthetic division to perform the division.   x^3+5x^2+8x+6 over x+3

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Q: Verify the factorization by using synthetic division 3x3 - 5a2-4x + 4 = 3(x+ 1)(x– 2)(x –) Verify…

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Q: A simplified polynomial that has exactly one term is called a/an__________ .

A: A polynomial that has exactly only one non-zero term is called a monomial. Also, each term of the…

Q: Use synthetic division to find f (c) .

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Q: Divide x – x4 + 3x³ + 2x2 – x + 1 by x³ – x² + 1, finding the quotient q(x) and remainder r(x).…

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Q: After constructing a divided difference table, what is the order of the polynomial that can be used…

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Q: . If f(x) = x - 3x? – 2x + 5, use synthetic division and the Remainder Theorem to find f(-2).…

A: Given: fx=x4-3x2-2x+5

Q: If a third degree polynomial has a lone x-intercept at x a , discuss what this implies about the…

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Q: Find a polynomial that interpolates (-1,4) and (3,6), then find the value of f(x) at x=0 and x= 2.

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Q: Using MOSA method, what is the polynomial y1 for

A: Given,           y'=x+y2 if y(0)=2

Q: Write a general polynomial q(z) of degree n with coefficients that are bo, b,, b2, ..b,. What are…

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Q: show f(x)=x^3-x^2-8x+12 has no zero greater than 4 and no zero less than -4 using synthetic division

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Q: performs the synthetic (ruffini) division of -3x ^ 5 + 4x ^ 3 -5x +1 / x - 2

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Q: A simplified polynomial that has exactly one term is called a/an ............ ?

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Q: Use long division and express P in the form  P(x) = D(x) · Q(x) + R(x).   P(x) = 20x4 + 16x3 + 9x2,…

A: Explanation: Given that,  P(x) = 20x4 + 16x3 + 9x2,    D(x) = 4x2 + 1 We will follow some steps to…

Q: A simplified polynomial that has two terms is called a/an ............ ?

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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: EXERCISE 4. Evaluate the following using Rationalization Method. Show your solution. Vx² + 7 – 3 lim…

A: Given  The limits are 1.  limx→3x2+7-3x+32.  limx→0x+1-1x

Q: 1.The graphs of f(x) = (x+3)(x- 4) and g(x) = (x+ 3)(x- 4) Which graph represents which polynomial…

A: Given that:

Q: What is a polynomial in x?

A: The x happening in a polynomial is generally referred to as a variable or an indeterminate. When the…

Q: Solve (x^3-4x^2+7x-10)\(x-2) using synthetic division.

A: Take the constant term of the divisor with the opposite sign and write it to the left. Write the…

Q: Use synthetic division to show that f(x) = x³ + 3x² – 13x – 15 is divisible by the linear factor x +…

A: Given query is to use synthetic division on f(x) , and find its factors.

Q: Write a polynomial with zeros 0,-3, and 2 with multiplicities 2. 1, and 2, respective What is its…

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Q: Find a polynomial of the specified degree that has the gi Degree 4; zeros -2, 0, 2, 4

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Q: Give the degree of the polynomial. 7 9 -vy

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Q: Part 1 of 2 Classify the polynomial as a monomial -8x+ 16 Choose the correct type of polynomial…

A: As this polynomial is having three terms.

Q: A simplified polynomial that has exactly one term is called a/an

A: Given: A simplified polynomial that has exactly one term is called a/an ......... Concept Used: A…

Q: Q3: Factorize f (x) = 2x* + x³ + 2x + 4 € Z5[x] as a polynomials product to irreducible over Z5?

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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: II. Use synthetic division method to finc the solution on the space provided. Set A 1. (x³ – 3x² +…

A: Given is (x3-3x2+5x+3)÷(x-3) The solution is provided below

Q: Using Taylor's theorem, formally represent 2x° +x* – 3x³ +x² – 5x +1 as x+1.

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Q: (6x* + 10z³ + 5x² + x + 1) ÷ (x + ,) 31

A: Use Synthetic division to find quotient

Q: Is x+ 4 a factor of f(x) = x5 + 10x4 + 29x3 – 28x2 (Use Synthetic Division in conjunction with the…

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Q: what could be a polynomial with a degree of 5 if its zeros are -2,1, and 4?

A: The given zeros are, –2, 1 and 4.

Q: 4) Use polynomial long division. 8 – 14r2 + x 2x – 3

A: The expression is 8x3−14x2+x2x−3.

Q: f(x) = x + 5x3 - 7x2-29x + 30 %3D

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Q: Find the conditions that the zeroes of the polynomials Ax) =x – px+ qx – r may be in arthametic…

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Q: 5) Write a rule for the 6th degree polynomial 8(x) pictured at right, whose only roots are -5, -2,…

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Q: 2. Find a polynomial that interpolates (-1,4) and (3,6), then find the value of f(x) at x=0 and x=…

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Q: Exercises: 1. Using the fact that 3x² +7x – 9 = ((((3)x) + 7)x) – 9), show how to produce this…

A: To find: number of smallest steps used in producing x8 +x4

Q: Find a polynomial of degree 3 that has zeros 5, -5, and 8

A: Given :To determine the polynomial ofdegree 3 has zeros 5,-5 and 8.

Q: Consider the division f(x) ÷ (x – k) where f(x) = (x + 8)²(x – 8)(x + 5)³. (a) What is the remainder…

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Q: Find the quotient using synthetic division. BE AE 35. (2x +3x+4x² +24x-45)+ (x+3) 36. (x* -5x'…

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Q: Divide using synthetic division. f(x) = (6x - 2x³ + 4x² – 3x + 1) + (x - 2) 187 6x + 12x3 + 22x2 48x…

A: We will use the method of synthetic division.

Q: 23 2. If the result of a polynomial division is 2x3 – 4x2 – 5x + x + 2 make at least three…

A: The result of the polynomial division is, 2x3-4x2-5x+23x+2 Let, f(x)=2x3-4x2-5x+23x+2…

Q: 1.  Use synthetic division to perform the division 4x3−15x2+10x−10 / x−1.

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Q: Use synthetic division to solve (x' +5x² +5x-2)÷(x+2). x' - 3x – 1 — Зх x – 3x +1 O x +3x-1 х* +3x—1…

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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.