11. If f(x) = -3x2 - 4x + 1, use synthetic division to evaluate f(4) 12. If x=-1 is a root of x + 4x? -x -4 =0, use synthetic division to factor the polynomial completely and list all real solutions of the equation.

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: How do I complete the square on thsi following polynomial: x2-6x+12-y=0 To end up with:…

A: x2-6x+12-y=0 cannot be expressed as (x-3)2+4-y=0 because (x-3)2+4-y=0 when expanded will give…

Q: To divide x^3+5x^2-2x+8 by x-5 using synthetic division,the first step is to write

A: According to question we have to calculate x3+5x2-2x+8x-5 By synthetic division

Q: When dividing x^3+2x+4 by 3x+2 in Z11[x], the remainder is

A: 1)  The statement is true  Now to see  ho the given polynomial is irreducible or not

Q: Choose the division problem that cannot be done using synthetic division. (a) 2x – 4x? + 6x – 8 is…

A: To choose which of the given division problems cannot be done using synthetic division. Synthetic…

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: 4. If x=-4 and x=1 are the roots of x* + 3x' - 3x +3x – 4 = 0, find the other two roots of the…

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Q: When dividing x^3+2x+4 by 3x+2 in Z5[x], the remainder is None of the choices 2

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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: 2. If the polynomial f (x) divided by (x – 3) gives a remainder of -1, then the remainder of…

A: Solution is given below:

Q: Prove that x- 3 is a factor of the polynomial x + 4x-17x2-14x + 6 without referring to the graph.

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Q: 9. When the polynomial mx' – 3x² + nx +4 is divided by x - 3, the remainder is 16. When it is…

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Q: In Problems 16–18, use the Rational Zeros Theorem to find all the real zeros of each polynomial…

A: (16) All the coefficients of the f(x) are constant. Use the Rational Zeros theorem to determine the…

Q: In Problems 21–32, determine the maximum number of real zeros that each polynomial function may…

A: Since you have posted multiple questions, we solve the first problem for you, if you want any…

Q: Find the zeros of f(x) = x² Enter your values separated by a semicolon. Do not include x = in your…

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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: Now let's attempt to work a similar problem backwards. Suppose you have a polynomial with leading…

A: Given  Leading coefficient =12 constant=15

Q: Find the polynomial in x of the third degree, which vanishes when x=-1 and x=2 has  the value 8 when…

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Q: For the remainder of the division of x-2x²+3kx+18 by x-6 to be equal to zero, k must be equal to?

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Q: 12. If x=-1 is a root of x + 4x? -x -4 =0, use synthetic division to factor the polynomial…

A:

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: 5) If the leading term of a polynomial is -2x18, what do you know about the end behavior? As x → 0…

A: We will find the end behavior of the polynomial when Leading term is given.

Q: Suppose 34 is a root of a polynomial equation. What does this tell us about the leading coefficient…

A: we have been given that the root of a polynomial equation is 34. we have to tell about the leading…

Q: 9. Find the quotient and the remainder of x³ + 2x² – 1 divided by 3x2 +1 in Z7[x].

A: Note that for Z_7  Any number is equal to the remainder when it is divided by 7.

Q: The equation y = 4r + 20z2 19z + 30 has one root at x = -6. Use synthetic division to find a…

A: Given:  The equation is y=4x3+20x2-19x+30   One root x=-6  Using synthetic division method the…

Q: For what value of a will five of the six real roots of 6x6 + 7x5 _ 43z4 - 153 + 49z2 + ax polynomial…

A: For what value of a will five of the six roots of polynomial P(x) be shared by the polynomial Q(x)

Q: Suppose a polynomial of degree 4 with rational coefficients has the given numbers as zeros. Find the…

A: Surd zeros are always in pairs. That is a+b is zero then a-b is also a zero of the polynomial.…

Q: 9.)-2, 5 -3.2 3

A: Since you have posted a multiple question according to guildlines I will solve first question (i.e…

Q: 2. Determine the polynomial equation with integral coefficients whose roots are -1, -2, and -3.

A: Answer and explanation is given below

Q: 4. Is it possible for a 6th degree polynomial with real coefficients to have 6 imaginary solutions ?…

A: To explain about the polynomial

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: 10) If x = 1 is a zero, what are the other zeros for x3 - 3x2 + x + 1 = 0 ?

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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: 47. a) If (x – 2) is a factor of 2x – 3x + k, find k. - b) When ax – 4x² + 5x – 3 is divided by (x +…

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Q: - Find The polynomial of degree 7 which has only the following zeros: 2( multiplicity 4), 4(…

A: Given: Degree of polynomial is 7. The given zeros of the polynomial are, 2 with multiplicity 4 can…

Q: Suppose that a polynomial function of degree 4 with rational coefficients has the given numbers as…

A: It is mentioned that the function is a polynomial of 4th degree. It means there will be 4 roots of…

Q: 1. Write the equation to the polynomial with double roots at 3 and 6, that levels off as it passes…

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Q: #7: For what value of k will the polynomial function f(x)=x'+6x² +kx=4 have the same remainder when…

A: The Polynomial Remainder theorem states that if x-b divides the polynomial, Qx, then the remainder…

Q: 8. Find the sum of all the zeros of the polynomial f(x) = x + 2x2-5x-6 O -5 -2 0. 2 6

A: Given equation is fx = x3+2x2-5x-6Comparing it with ax3+bx2+cx+d = 0a = 1, b = 2, c = -5, d = -6

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: 8) If x = 2 is a zero, what are the other zeros for x3 – x2 - x- 2 = 0 ?

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Q: If x = -1 is a root of the polynomial 0 = æ³ + 2x2 – 5z – 6. what are the other roots? Ox =-3, x = 2…

A: see next step

Q: If a polynomial f(x) when divided by (x - a) gives a remainder r₁, and when divided by (x - b) gives…

A: Given that fx is divided by x-a, we get remainder r1, so there exist a polynomial qx such that…

Q: Use synthetic division to divide (5x^4 - 2x^3 + x - 4) by (x -2)

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Q: x to the third minus 512 over x-8 and must be solved using synthetic division.

A: First of all, consider the dividend and the divisor.

Q: Suppose a polynomial of degree 4 with rational coefficients has the given numbers as zeros. Find the…

A: Zeros of a polynomial: Let the other zero be kThen the equation of the polynomial…

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

Q: 8. Match the polynomial equation in Column A with the correct rational zeros in Column B. Column A…

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Q: 17) Perform the following division of polynomials by synthetic division. (x* – x³ – 9x² + 29x – 30)…

A: Given (x4-x3-9x2+29x-30) ÷ x2-3x+4